Research projects

Theme: Accelerator Physics | Supervisor: William Bertsche

One of the outstanding grand challenges in physics is to understand the fundamental differences between matter and antimatter that have left us with a universe that is largely composed of matter. The ALPHA experiment at CERN seeks to address this question by performing precise atomic physics measurements on trapped antihydrogen atoms in order to seek minute differences with equivalent measurements in hydrogen. The collaboration is building ALPHA-g, the next generation of antihydrogen traps intended to measure antimatter gravitation.

We are seeking a PhD student to design and perform gravitational free-fall measurements on antihydrogen atoms in order to directly measure antimatter gravitational acceleration as a test of the weak equivalence principle. The student will design and analyse experimental protocol and diagnostic technique for use in ALPHA-g intended to measure the gravitational acceleration g of antimatter on Earth. The student will also be expected to participate in ALPHA's general experimental programme with trapped antihydrogen atoms.

This is an interdisciplinary experimental project based at CERN with underpinnings spanning plasma, atomic and particle physics. The successful realisation of this project will require both experimental efforts as well as development of diagnostic tools for measuring and controlling the probe and background magnetic fields in the experiment. Particle and field behaviour will be modelled using software such as GPT, Opera, ANSYS and COMSOL. This is a 3.5 - year fully-funded PhD studentship with the University of Manchester where the majority of the studentship would be based at CERN in Geneva, Switzerland.

Theme: Accelerator Physics | Supervisor: Robert Appleby

We are very excited to design and build an upgraded Large Hadron Collider to make proton- proton collisions at a much higher collision rate, to probe the fundamental structure of matter, measure the Higgs boson and other new particles to an unprecedented level of precision and search for undiscovered particles of nature. There are often opportunities for students to participate in research in this area, on novel new cavities, such as crabbing cavities, on collimation, and on the beam dynamics of transporting high energy beam throughout the LHC. This research has analytical, simulation and experimental aspects to it.

Theme: Accelerator Physics | Supervisor: Guoxing Xia

The development of plasma accelerators has achieved significant breakthroughs in the last three decades. Nowadays, the laser wakefield accelerator can routinely produce ~GeV level electron beam with percentage energy spread within only a few centimetre plasma cell and the accelerating gradient (~100 GeV/m) achieved is over three orders of magnitude higher than the fields in conventional RF based structures (in general less than 100 MeV/m). The electron beam driven plasma wakefield acceleration has successfully demonstrated the energy doubling of the electron beam (from an initial 42 GeV to a final 85 GeV) at the Stanford Linear Collider-SLC within an 85 cm plasma channel. A very recent proton driven plasma wakefield acceleration-AWAKE experiment at CERN has achieved for the first time ever the electron acceleration in a proton-driven plasma wakefield1 [1]. All these achievements will revolutionize today's conventional particle acceleration technology and will be paving the way for next generation very compact and cost effective energy frontier particle accelerators or colliders based on this enabling plasma technology.

Our group is one of the first few proponents to propose the proton driven plasma wakefield acceleration experiment (CERN AWAKE). Currently we are focusing on several exciting research activities including proton beam, electron beam and laser driven plasma wakefield acceleration and advanced dielectric structure based particle accelerators. Through collaboration with CERN (on AWAKE), Daresbury Laboratory (electron driven plasma wakefield acceleration) and DESY in Germany (through the EU-funded EuPRAXIA project on laser wakefield acceleration) and other international labs, we are working on various topics related to plasma and dielectric structure based novel particle accelerators and radiation sources.

Projects:
• Proton-driven plasma wakefield acceleration - AWAKE at CERN.
• Key issues in electron driven plasma wakefield acceleration - Daresbury Lab.
• A compact plasma beam dump for next generation particle accelerators.
• Ultrashort electron beam driven dielectric wakefield acceleration.
• Smith-Purcell radiation based on ultrashort electron beam in grating structures.
• Accelerator on a chip - laser driven dielectric accelerator.
• Compact radiation sources (x-rays and gamma-rays) based on intense laser plasma interaction.

Theme: Accelerator Physics | Supervisor: Darren Graham, Robert Appleby

Terahertz radiation, which sits between infrared and microwave radiation on the electromagnetic spectrum, has the potential to reduce the size and cost of particle accelerators, opening the door to new applications in compact medical therapy, security screening, and fundamental materials science with ultrafast electron or x-ray pulses. We are seeking PhD students to work on terahertz driven particle beam acceleration, joining a collaborative project at the Cockcroft Institute. The primary objective of this project will be to optimise high power ultrafast laser based terahertz radiation sources and investigate novel concepts for terahertz-based manipulation of the 5-50 MeV relativistic electron beams provided by the VELA accelerator at STFC Daresbury Laboratory. By developing new concepts for acceleration we seek to enable a new generation of table-top particle accelerators.

The Institute has been heavily involved in the design, commissioning and operation of the Versatile Electron Linear Accelerator (VELA) facility which is capable of delivering a highly stable, highly customisable, short pulse, high quality electron beam to a series of test enclosures.

This project will involve using a number of high-power ultrafast lasers, including state-of-the- art femtosecond laser systems in Dr Graham's lab at the Photon Science Institute, a Terawatt laser system at the Cockcroft Institute, and high-energy particle accelerators at STFC Daresbury Laboratory. Hands-on experience in the use of lasers and optical components is not essential, but the student is expected to have a keen interest in experimental physics.

Theme: Accelerator Physics | Supervisor: Roger Jones

Very high energy electrons (VHEE) have the potential to deliver radiotherapy rapidly, in a well- controlled manner, and with a more favourable dose distribution than conventional photon therapy, or indeed extant radiotherapy techniques. In addition, the technological advantages of rapid dose delivery, there may well be significant radiobiological advantages in terms more efficacious tumor control or indeed other target control for similar doses as that used in conventional radiotherapy. It is important to realize that VHEE can effectively "freeze" the patient motion, as the beam can be steered rapidly using deflectors familiar to those in RF engineering. This Ph.D. project will have analytical, simulation, and experimental aspects. It will necessarily entail both mathematical physics and medical physics.

In order to assess the potential benefits of VHEE over extant methods we need to investigate the dose distribution in phantoms, and the applicability of beam steering focussing and various other beam delivery aspects. In each case, this necessitates intensive computing, based upon application of Monte Carlo methods to track the particles within the media. Here we will utilize the well-known and well-validated code Geant4, Topas, and related codes to investigate the dose distribution in heterogeneous media. We plan to capitalize on massively parallel computing and special dose collation techniques.

Our short-term plans entail validating the dose delivery to water phantoms -with the experimental component being obtained via the unique facility in Daresbury laboratory known as VELA/CLARA (which is anticipated to allow experiments at 50 MeV in 2018). We will also consolidate initial experiments made by our students in this area with additional experiments at 250 MeV with the CALIFES (recently renamed CLEAR) facility at CERN. Based on these validations on dose-depth delivery we will also proceed to investigate, both with intensive simulations and with experiments at the aforementioned facilities, focusing within water phantoms. Initial simulations indicate that VHEE radiotherapy is insensitive to media intervening in between the path of the particle beam and that of the intended dose delivery point of cancerous tissue -i.e. it is insensitive to heterogeneities such as bone tissue, air bubbles and related materials. This is a significant advantage for particular radiotherapy treatments (such as lung and bowel for example) over extant radiotherapy treatments.
High-energy electron radiation therapy has important implications for a novel radiation treatment system for cancer. It may have significant benefits over other means of radiotherapy treatment. The CLARA facility at Daresbury Laboratory (DL) provides a unique facility to provide ground-breaking experiments in this area. There is opportunity for publication in high quality journals in this area.

Theme: Nuclear Physics | Supervisor: Kara Lynch

What is the shape of the nucleus in the moments before it emits a proton? How does the shape of the nucleus change when the proton becomes unbound?

Aim: This project aims to perform the first laser spectroscopy studies on proton-emitting nuclei, in order to measure the shape and other nuclear properties of these exotic species.
Details: At the edges of the nuclear landscape, a rare form of radioactive decay occurs where the nucleus emits a proton. Studying proton-emitting nuclei with laser spectroscopy provides an opportunity to measure their nuclear properties and understand the behaviour of nuclei right at the limits of nuclear existence.

Laser spectroscopy measures the hyperfine structure of atoms, an atomic fingerprint that allows nuclear properties (e.g. spin, electromagnetic moments and charge radii) to be measured in a nuclear-model-independent way. For example, the charge radius tells us about the proton distribution in the nucleus i.e. its shape. By measuring nuclei across the proton-drip line (beyond which proton decay occurs), we can understand the effect of the proton on the nucleus before it is emitted and gain a unique insight into how this single proton can influence the behaviour of the whole nucleus.

This project will be carried out at ISOLDE (CERN) and a new facility at Michigan State University (USA). It will use state-of-the-art laser spectroscopy techniques, such as Collinear Resonance Ionization Spectroscopy (CRIS) and the newly developed PI-LIST setup, to measure the properties of proton-rich nuclei. There are Ph.D. studentships available in the areas of laser spectroscopy and decay spectroscopy. There is an opportunity in the project for students to spend a large fraction of their time at CERN.

Theme: Nuclear Physics | Supervisor: Sean Freeman

The introduction of the spin-orbit interaction by Maier and Jensen led to an understanding of the observed shell gaps and magic numbers in near-stable nuclei. The appearance of these ideas in undergraduate textbooks gives the impression of solidity and permanence to the well- known sequence of magic numbers. Recent observations, however, have challenged this basic assumption by suggesting that the sequence of single-particle states observed near stability is actually quite fragile; studies of nuclei far from the line of β stability have begun to indicate that the familiar shell gaps do not persist in exotic systems. Instead, shifts in the sequence of single-particle levels conspire to give gaps that change with changing nucleon number, fundamentally reshaping the basis of nuclear structure and producing new and unexpected phenomena. The reasons for these alterations to one of the basic tenets of nuclear physics are currently being debated and are of paramount interest in the development of the understanding of atomic nuclei.

Single-nucleon transfer reactions offer a suitable probe of the single-particle characteristics via the spectroscopic factor (SF), measuring the overlap of the wave function of a state with simple single-particle configurations. Being subject to sum rules, SFs allow access to the occupancies of underlying single-particle orbits.

PhD projects in this area will involve using transfer reactions with radioactive beams to investigate the evolution of single-particle structure in to exotic regions of the nuclear chart. his work will predominantly take place at HIE-ISOLDE, CERN using the newly commissioned ISOLDE Solenoidal Spectrometer (ISS).

Theme: Nuclear Physics | Supervisor: Gavin Smith, Tobias Wright, David Sharp

Projects involve the measurement of fission data from the Neutron Time-of-flight (n_TOF) facility at CERN. Neutrons of a broad spectrum of energies are produced by spallation of protons on a lead target. The neutrons are timed relative to the proton pulse and are used to induce fission on an actinide target in experimental area of the n_TOF facility. TheSpectromeTer for Exotic Fission Fragments (STEFF) is a 2E-2v detector system, developed at the University of Manchester, which used to study the resulting fission fragments. It allows measurement of the velocities and energies of both fragments from the fission event. Mass may be measured independently in each arm. STEFF includes an array of 12 (5"x4") NaI scintillation detectors for gamma-ray detection. The fission fragments stop in Bragg detectors, the outputs of which are digitized as a function of time and are used to measure energy loss (dE/dx) and range; and hence are used to determine atomic-number distributions. The measured properties of fission and fission-fragment gamma decay are used in studies of the dynamics of the process and have applications in the nuclear-energy sector.

A new programme is commencing to use the ISOLDE Solenoidal Spectrometer facility at CERN to use (d,p) reactions in inverse kinematic to induce fission in previously unaccessible systems to neutron irradiation techniques.

Theme: Nuclear Physics | Supervisor: Kieran Flanagan-

How three-nucleon forces influence nuclear structure and the limits of nuclear existence remains a compelling question in nuclear physics. There are currently many different approaches being utilized around the world to measure the properties of nuclei that may help answer this question. Since laser spectroscopy measures nuclear observables without introducing any assumptions associated with a particular nuclear model it has become a very popular method. Until recently it could only be used to study isotopes that are produced in relatively large amounts, which has limited its application. Over the last 5 years the CRIS collaboration at CERN has developed new techniques in laser spectroscopy that have permitted measurements on beams of less than 10 atoms per second. This has greatly extended the reach of laser spectroscopy and has allowed it to study the most exotic nuclei for the first time.

The project will be carried out at the ISOLDE facility, CERN, which is the premier radioactive beam facility at the precision frontier. There are currently PhD student projects in the area of ion trapping, production and application of negative ions for nuclear research and atomic physics. There is an opportunity in the project for students to spend a large fraction of their PhD at CERN.

Theme: Nuclear Physics | Supervisor: Paul Campbell-

Aims: this project aims to measure fundamental nuclear properties in exotic super-asymmetric fission fragments and atomic-nuclear processes in ultra-low lying nuclear excited states.

Details: The project is to be based at the IGISOL facility, JYFL, Jyvaskyla, Finland and ISOLDE, CERN. The research will exploit a recently constructed electrostatic ConeTrap and use it, for the first time, to facilitate high efficiency laser spectroscopy and then to use the developed spectroscopy to make precision measurements of nuclear parameters via the hyperfine structure and isotope shift.
The project is based at facilities where The University of Manchester and our national and international collaborators, from the UK, Belgium, Finland, Germany, Russia and Japan, have performed successful nuclear structure (and atomic) studies for many years. In the new work our objective is however to achieve spectroscopic efficiencies at an order of magnitude higher than that we have previously attained. Historical efficiencies have permitted in-flight studies of short-lived radioactive ions with lifetimes as short as 10 ms and production rates as low as 10 ions per second. We now intend to supersede these efficiencies and be capable of studying the most weakly produced and highest Z systems available at our on-line isotope separators.

Theme: Nuclear Physics | Supervisor: Tobias Wright

The process of nuclear fission has been exploited as a virtually carbon-free energy source for many decades and it is set to play a major role within future global energy supplies. Advanced Nuclear Technologies (ANTs) are being developed which will serve to provide cheaper, safer and more efficient energy from nuclear fission. These advanced technologies will use new forms of nuclear fuel and designs of reactor which bring inherent technical and scientific challenges which must be tackled to ensure success. Specifically, a complete understanding of the physics governing the many processes involved within these technologies must be obtained. This understanding will come from detailed simulations and calculations and underlying these are the input of nuclear data. These nuclear data quantify all the associated nuclear reactions that occur and govern the functionality of these systems. These data sets typically arise from detailed experiments which measure individual quantities to appropriate accuracies. It is acknowledged that the current nuclear data is not of adequate accuracy for ANTs.

Uranium Nitride fuel is being considered as an Accident Tolerant Fuel for use in GenIV reactors and there is a requirement to improve the nuclear data on nitrogen. In particular, nitrogen enriched in 15N is being considered which is a poorly-studied isotope from a nuclear data perspective. Measurements of the neutron scattering, capture and n,p cross sections on 15N will improve this. The neutron time-of-flight facility n_TOF, CERN, is a world-leading cross section measurement facility and well-suited to performing these types of measurement of neutron-induced cross sections in the required energy region. Further, the neutron source ISIS at the Rutherford Appleton Laboratory is well suited for performing neutrons scattering measurements so use of this will be pursued. Projects will also investigate nuclear data measurements of importance to ANTs on neutron capture and fission.

Theme: Nuclear Theory | Supervisor: Judith Mcgovern, Mike Birse, Niels Walet

The Nuclear Theory at Manchester is interested in the connections between nuclear physics and the underlying theory of the strong interaction, Quantum Chromodynamics (QCD), and also in descriptions of nuclei from first principles. Our work ranges from studies of the properties of a single nucleon, through descriptions of the forces between two or three nucleons, to calculations of heavier nuclei. Key tools in this work are effective field theories (EFTs). These theories are expressed in terms of the relevant low-energy degrees of freedom, such as nucleons, pions and photons. They incorporate the symmetries of QCD including a chiral symmetry which reflects the existence of almost massless up and down quarks inside hadrons. This symmetry places important constraints on the interactions of pions with other particles. The work combines ideas from quantum field theory with methods for treating few- and many-body systems. It involves a combination of analytic and numerical calculations, the exact balance depending on the particular project. Possible projects are available on all of the topics listed below for individual members of staff.

Dr Judith McGovern's current interests are focussed on applications of chiral EFTs to the properties of protons and neutrons, and in particular to their electromagnetic polarisabilities. These quantities describe the response of a nucleon to external fields. Recent work has been on analyses of Compton scattering data for the proton and deuteron; extensions will determine the full range of proton and neutron polarisabilities from new experiments on protons and light nuclei. The same approach can be used to determine the contribution of two-photon exchange to the Lamb shift in muonic atoms. In work with Mike Birse, it has been applied to muonic hydrogen, and further work is needed to analyse recent experiments on other muonic atoms. The results of this will help to shed light on the "proton radius puzzle".

Prof Mike Birse works on nuclear forces within the framework of EFTs, and their applications to few-nucleon systems. A particular interest is the use of the renormalisation group to analyse the scaling behaviour of the interactions. In collaboration with Niels Walet, he is also developing an approach to many-body systems based on a functional version of the renormalisation group. This provides a tool for handling strongly interacting systems that does not rely on diagrammatic expansions.
Prof Niels Walet has expertise with a variety of first principles approaches to many-body systems, in particular the coupled-cluster method. In work with Mike Birse, he has implemented a stochastic variational method to calculate the properties of few-nucleon systems. First applications of this have been made using simpler EFT without pions to describe nuclei with up to eight nucleons.

Theme: Particle Physics - Experimental | Supervisor: Michaela Queitsch-Maitland, Elena Gramellini

The Experimental Particle Physics group at the University of Manchester is looking for excellent applicants to fill prestigious PhD positions in Experimental Particle Physics (https://www.hep.manchester.ac.uk/study/ ).

Our group (https://www.hep.manchester.ac.uk/) is one of the largest research groups in the UK with over 100 members, composed of both world-leading experimental and theory research groups.

Our experimental research takes place within large international collaborations and spans the energy frontier (ATLAS, FCC), quark flavour (LHCb, BES-III), lepton flavour (g-2, Mu2e), neutrino physics (DUNE, MicroBooNE, SBND, SuperNEMO, FASER) and the dark sector (Darkside-50, Darkside-20k, FASER). We also carry out research into new detector technologies and new data acquisition strategies for future experiments. We host one of the largest and most successful Tier-2 distributed computing centres in the UK.

We are accepting applications for various fully-funded PhD studentship schemes. Further details about each PhD scholarship can be found at https://www.hep.manchester.ac.uk/study/. Candidates who are eligible for multiple schemes do not need to submit separate applications for each: it is however useful to indicate in your application the schemes you believe you are eligible to apply for.

Most studentships are expected to start in October 2025 but options for early or delayed start are possible, subject to available funding.

Studentships cover tuition fees plus a tax-free yearly stipend to cover living expenses. All students will be provided with all necessary resources to do their research, including a laptop, access to our local distributed computing facilities, a dedicated training programme, and a supervisory team. Most students will have the opportunity to spend around one year fully-funded at the experimental site (e.g. CERN, Fermilab). In addition, a separate Research Training Support Grant will be awarded for travel and subsistence to attend conferences, summer schools, and working meetings throughout the PhD programme.

We run a competitive selection process in two steps, first evaluating candidates based on CV and research/professional experience, followed by interviews with a gender mixed panel. The minimum requirement for application is a strong 2:1 class UK Masters honours degree or equivalent. Substantial professional or research experience is advantageous.

The starting point for all applications is the portal https://www.manchester.ac.uk/study/postgraduate-research/programmes/list/05510/phd-particle-physics/. Interested applicants should also contact the Particle Physics postgraduate coordinators: Dr. Elena Gramellini (Elena.Gramellini@manchester.ac.uk) and Dr. Michaela Queitsch-Maitland (Michaela.Queitsch-Maitland@manchester.ac.uk) to register their interest in one or more schemes.

Theme: Particle Physics - Experimental | Supervisor: Justin Evans, Elena Gramellini

The Deep Underground Neutrino Experiment (DUNE) is an international collaboration of scientists from more than 30 countries with the goal to study neutrino interaction and to discover CP violation in the lepton sector of the Standard Model, addressing the fundamental question of matter dominance in the Universe. It will also study neutrinos from supernova explosions and search for other non-standard physics phenomena, such as proton decay.

Our group plays a leading role on the project: we are responsible for building one of the largest components of the detectors, large wire planes (called Anode Plane Assemblies) that will read out the charge produced by neutrino interactions in the liquid argon of the DUNE far detectors located in South Dakota. We are also starting a programme to develop the next-generation charge readout designs, using a pixel design that will allow us to measure "true" 3D images of the interaction (see SoLAr and QPix in the R&D session). Potential PhD projects could be related to the optimisation of the design of such a detector, building and testing of detector components, or the developments of algorithms for the reconstruction of the images. Another important aspect is the development of physics analyses using machine learning techniques. As we are also collaborate on the short-baseline neutrino programme (see separate section), which uses similar detector techniques, data from these detectors could be used to validate and further develop physics analyses with a focus on searches for physics beyond the Standard Model.

Theme: Particle Physics - Experimental | Supervisor: Jamie Mcdonald

Dark matter remains one of the greatest unsolved problems in modern physics. The successful candidate will have the opportunity to work on a new experimental programme beginning at the University of Manchester to develop a detector to search for dark matter axions. Axions are now some of the most sought-after particles in fundamental physics, with a huge network of international experiments seeking to detect them. Axions can explain both the strong-CP problem and act as natural dark matter candidates.

Theme: Particle Physics - Experimental | Supervisor: Michaela Queitsch-Maitland

The FASER experiment at CERN's Large Hadron Collider (LHC) is designed to explore new territory in particle physics by detecting light, weakly interacting, and long-lived particles produced in the very forward region of proton-proton collisions. It also provides the first opportunity to study collider-produced neutrinos of all flavours at TeV energies, with important implications for forward QCD modelling and astroparticle physics, including cosmic-ray air-shower modelling. Notably, FASER also has the capability to detect anti-tau neutrinos for the first time.

This PhD project will involve contributing to data processing and analysis, as well as detector maintenance and operation. There will also be opportunities for hands-on experience with hardware and R&D for future detector upgrades. Possible areas of focus include precision measurements of high-energy neutrino interactions and charged-particle track reconstruction. The student will work closely with the University of Manchester's particle-physics group and the international FASER collaboration, with opportunities for extended periods at CERN.

Theme: Particle Physics - Experimental | Supervisor: Mark Lancaster

Neutrinos have already taken us beyond the Standard Model of Particle Physics, and may well be ready to reveal yet more new physics beyond the Standard Model. Our group is active in several key areas of neutrino research. We are involved in the US-based liquid argon programme, which includes the Short Baseline Neutrino (SBN) Programme that is searching for the sterile neutrino -a completely new particle; and DUNE, a long-baseline experiment with a cathedral-sized detector, which aims to explain the matter-antimatter asymmetry of the University through observations of neutrino oscillations. Another important question is whether the neutrino can be its own antiparticle, a so-called Majorana fermion. In this case it should be possible to observe an extremely rare radioactive decay called neutrinoless double- beta decay, which would violate lepton number conservation -we are searching for this process with the SuperNEMO detector in France and with NEXT in Spain. We also have an active detector instrumentation efforts that aim to enhance noble element detectors for future experiments

Theme: Particle Physics - Experimental | Supervisor: Chris Parkes, Ivan Polyakov, Michel Decian, Conor Fitzpatrick-

LHCb searches for physics beyond the Standard Model through the analysis of beauty and charm quarks. The Manchester LHCb group is responsible for world leading analyses, detector commissioning and operations, and future R&D.
Students are typically involved in two of the following areas.

Flavour physics:

There are research projects in all our main areas of focus: matter- anti-matter- asymmetries (CP violation), precision tests with semileptonic decays, and rare decays. The group's work has been instrumental in the landmark discovery of CP violation in charm decays. The group leads several measurements of CP violation of B hadron decays many of which are sensitive to the CKM angle gamma.

Other areas of significant interest are measurements using semileptonic decays of charm and B hadrons, which primarily focus on tests of lepton universality, a fundamental principle of the Standard Model that has seen tensions in recent measurements, and rare decays involving lepton-flavour violating processes.
A recent analysis of charm decays led to over 20 world's best limits.

Our group has been the first to exploit GPUs in an LHCb analysis and have pioneered fast simulation methods that are now responsible for most simulated events in LHCb. We have leading involvement in LHCb's Real-Time Analysis from the outset and remain committed driving novel analysis approaches. All our projects include a high degree of data science applications and training. We are in close contact with theory colleagues who work on the phenomenology of the LHCb physics programme.

Exploiting the upgraded LHCb experiment:

The LHCb experiment has been upgraded to a new detector for higher luminosity operation and our group is strongly involved in commissioning and operation of the experiment, especially of the LHCb Vertex Locator (VELO). Our group built about 80% of the individual VELO modules. The detectors are based on silicon pixels with an innovative micro-channel cooling system. Research projects in this area include monitoring the data quality, studies of radiation damage, and improvements to data reconstruction and simulation.
We have a leading role in the implementation of LHCb's real-time trigger, alignment and calibration system, which produces ready-for-analysis data straight out of the detector. Future projects in this area will focus on achieving an optimal trigger quality, efficiency and throughput, as well as micron-level alignment of detector components.

Designing the long-term future of LHCb:

The group is involved in developing future detector systems. One is a new semiconductor detector to be used in the innermost regions of the downstream tracking stations. Projects in this area will play a key role in the construction and evaluation of prototype detector elements.
The second system is a novel vertex detector that can deliver precise timing information and can cope with a factor ten more particles compared to the current pixel LHCb VELO. Projects will focus on advanced electronics and sensor technology, novel cooling and support structures, and 4D reconstruction of particle tracks.

Theme: Particle Physics - Experimental | Supervisor: Mark Lancaster

The Mu2e experiment at Fermilab aims to improve the sensitivity in the search for neutrinoless muon-to-electron conversions (in nuclei) by four orders of magnitude. The rate is such conversions is essentially zero in the Standard Model and thus any observation would be a signal of new physics. The experiment is sensitive to a wide variety of new physics phenomena many of which cannot be directly detected at the LHC and is particularly timely given hints from the Fermilab muon (g-2) experiment and LHCb that muons are perhaps not quite behaving as predicted by the SM. Our group is responsible for commissioning and operating an X-ray detector to record the number of muons captured by the target (in excess of 108/sec) in collaboration with other UK groups.

The FNAL Mu2e Experiment
In this project, a student will be commissioning the X-ray detector with the first muon beam and optimising its performance and making a precise determination of the muon flux: without which, the rate or limit of new interactions beyond the SM cannot be determined. In parallel, the project will involve optimising the performance of the straw-tracking detectors to maximise the experiment's sensitivity to new physics phenomena and thus establishing the world's most sensitive search for charged-lepton flavour-violation.

Theme: Particle Physics - Experimental | Supervisor: Roxanne Guenette

The NEXT experiment uses a high-pressure xenon gas time projection chamber to search for Majorana neutrinos. This type of detectors allows for great energy resolution and offers imaging capabilities that can help reduce background, two essential ingredients for identifying the extremely neutrinoless double beta decay process. We are currently constructing a new phase of the experiment at the Laboratorio Subterráneo de Canfranc in Spain, NEXT-100 which will take data for the next few years, providing competitive limits on the neutrinoless double beta decay half-life and demonstrating the capability of the technology at larger scale. Our group will play an active role in the detector commissioning and will perform several data analyses. We will also work on developing a new readout plane for the future ton-scale phase of the project.

Theme: Particle Physics - Experimental | Supervisor: Elena Gramellini

The Manchester group is developing new technologies for future generation of detectors, especially in the context of noble element media: small scale cutting edge R&D today is the first step to unlock the discoveries of tomorrow. Currently, the group is focused on developing new cryogenic photodetector concepts (LILAr [arxiv.org] and Metalenses) and new charge readouts (Q-Pix [arxiv.org]). The Light Imaging in Liquid Argon (LILAr) project aims to develop coatings of amorphous selenium for the detection of VUV light in noble element detectors with high quantum efficiency in wide surface detectors. Metalenses are nanostructures that focus light, allowing for a cost-effective solution to increase the light collection while maintaining a reasonable number of photosensors in noble element detectors. Both projects have potential ties to material science and industry.

QPix is a novel ionisation readout and waveform digitisation scheme to pixelate kiloton-scale LArTPC detectors. With the SoLAr project, the group is also developing a new fully pixelated light-charge readout concept for the detection of low-energy solar or supernova neutrinos. As part of the QPix consortium, the group is in the process of building the "Pixel Lab": a University of Manchester space for the development of pixelated TPC technology. Table top experiments are extremely rare in particle physics: the Pixel Lab will give unprecedented opportunities to our students for hands-on work on detector R&D.

Theme: Particle Physics - Experimental | Supervisor: Elena Gramellini, Alexander Oh, Roxanne Guenette, Chris Parkes

R&D for Particle Detectors

Research and development in particle detectors is a foundational pillar of particle physics. Every major discovery in the field-from identifying new particles to probing the structure of the universe-relies on our ability to detect, track, and measure the faintest signals produced in high-energy environments. At Manchester, our detector R&D programme drives innovation at this frontier, developing the next generation of technologies that will power tomorrow's experiments in both fundamental science and real-world applications.

Theme: Particle Physics - Experimental | Supervisor: Alexander Oh, Andrew Pilkington, Yvonne Peters, Caterina Doglioni, Michaela Queitsch-Maitland, Terry Wyatt

ATLAS is a general-purpose particle physics experiment at the Large Hadron Collider (LHC). Manchester has played a major role in the ATLAS experiment for many years. In 2024, we expect to offer projects in the areas of electroweak physics, Higgs physics, and physics beyond the Standard Model.
The Manchester group has played a major role in studying the self-interactions of the weak bosons. Recent highlights include precision differential measurements of vector-boson scattering processes at a hadron collider, the first observation of photon-photon fusion processes, and the search for proton-proton collision events that contain three weak bosons. Each of these processes is sensitive to the self-interactions of electroweak bosons, which is a key prediction of the Standard Model, and deviations from the expected event rates would signify anomalous weak boson self-interactions: a smoking gun for new physics! The processes however are extremely rare and measurements are only becoming possible now, with the large datasets available from the LHC.
In the Higgs sector, we continue to develop new ways of understanding the interactions of the Higgs boson. Our group members made the first measurements of the Higgs boson differential cross sections and used these to search for anomalous Higgs boson interactions. We are also heavily involved in studying the relationship between the Higgs boson and the Top quark, with major contributions to the observation of Higgs bosons produced in association with a top-antitop pair. We currently lead measurements that probe the CP nature of the Higgs-Top interaction, which could provide the missing source of CP violation needed to explain the matter-antimatter asymmetry of the universe.
The Manchester group has been central to the development of new initiatives in the search for new physics phenomena, spearheading new approaches to the search for dark matter through precision measurements and through real-time data-analysis techniques. We lead new efforts to search for heavy Majorana neutrinos and other lepton number violating phenomena at the LHC through weak boson fusion processes, have developed novel observables to test the principle of lepton universality in W boson decays, and are the primary developers of the "Trigger-Level Analysis" technique to overcome the limitations of the data acquisition system. We have a broad direct search programme for new particles through multi-boson final states (searching for high mass particles like gravitons), di-tau final states, bb-tau- tau final states, and searches for rare low mass particles that would evade standard searches.
We have a close and long-standing connection between experimental and theoretical particle physicists. This provides plenty of opportunities for joint experiment-theory collaborations on LHC physics. We have had several very successful examples of PhD students developing a piece of phenomenology or a novel analysis technique in collaboration with the particle theory group, which they have then applied to the analysis of ATLAS data.
PhD students also contribute to ATLAS operations, i.e. developing the data acquisition system (the "trigger", improving hadronic jet reconstruction and calibration (including heavy-flavour tagging), and determining the properties of hadronic tau decays. We are also strongly involved in upgrading the ATLAS pixel detector for Phase-2. The PhD projects will combine activities from any of these research areas.

Theme: Particle Physics - Experimental | Supervisor: Justin Evans

The SBN Programme will combine three international experiments in order to perform the world's most sensitive search for sterile neutrinos, using the phenomenon of neutrino oscillation. Sterile neutrinos are hypothesized, new neutrino flavours, which do not interact via the weak force; they are only observable through their oscillations. SBN aims to search for such oscillations by placing three liquid argon TPC (LArTPC) detectors (MicroBooNE, SBND, and ICARUS T600) at short baselines along the Fermilab Booster Neutrino Beam and studying how the rates of different neutrino flavours vary as a function of the neutrino travel distance. This project will involve the analysis of data from the already running MicroBooNE experiment, as well as the commissioning of the SBND experiment, which is currently being constructed. Our group's focus is on reconstructing electromagnetic showers to search for neutrino oscillations, measuring neutrino cross sections and looking for alternative signatures of physics beyond the Standard Model. The project could also have a small hardware component through involvement in the commissioning of the SBND detector.

Theme: Particle Physics - Experimental | Supervisor: Darren Price

The DarkSide-20k experiment aims to discover dark matter via the elastic scattering of dark matter particles from space on argon nuclei in a 50-tonne detector instrumented with over 11,000 cutting-edge silicon photosensors operating at cryogenic temperatures.

DarkSide-20k is designed for a sensitivity reach to dark matter interaction rates more than two orders of magnitude beyond current searches at dark matter masses of 1 TeV and to have leading sensitivity to masses above the energy scale accessible at the LHC. This experiment is in the R&D phase and is expected to begin taking data at the Laboratori Nazionali del Gran Sasso in Italy in 2023. Manchester holds key responsibilities within the experiment. These include the construction of the high efficiency low radioactivity cryogenic silicon photosensor modules for the outer detector, and the design electrical tests and performance characterisation of these sensors, critical to enable discriminate dark matter signals from natural radioactive background processes. The Manchester group plays a central role in algorithm development, detector simulations, and the analysis of data from prototype detectors. The group plays a central role in the expansion of the science programme of DarkSide, publishing innovative studies in conjunction with theorists exploring prospects and strategies for studying non-standard dark matter models, expanding dark matter mass sensitivity down to the tens-of-MeV range, and exploration of neutrino physics opportunities with this detector. Potential PhD project work can combine aspects of detector design/construction, computer simulations, data analysis, and physics sensitivity studies.

Theme: Particle Physics - Theory | Supervisor: Jeffrey Forshaw

Almost all of the measurements at contemporary colliders, including the LHC, depend on precise theoretical calculations of the QCD "radiation" of quarks and gluons. That is because this radiation is ubiquitous in collisions involving coloured particles. The relatively strong coupling in QCD means that this physics is remarkably interesting because it cannot be captured by simple fixed-order perturbation theory. Instead "all orders" algorithms need to be developed and implemented. Here in Manchester, we are world-leading experts in all-orders QCD and this PhD project will involve joining a pre-existing team of researchers to work on the theoretical development and/or computational implementation of a new algorithm which will significantly improve upon anything that has gone before. Apart from its tremendous utility, this project involves analytic work in a problem of fundamental theoretical interest.

Theme: Particle Physics - Theory | Supervisor: Apostolos Pilaftsis

The Standard Model of particle physics has been extremely successful in describing all current experiments, but it leaves many questions unanswered, like why particles have the masses and other quantum numbers that they do, why there are three generations of elementary particles, why there is more matter than antimatter in the universe, what the 'dark matter' of the universe is made of, whether the three fundamental forces of particle physics can be unified, and whether this can be further unified with a quantum theory of gravity. To try to answer these questions, we bring together progress in theories Beyond the Standard Model (BSM) with a phenomenological understanding of how those theories could be tested in future experiments and how we can constrain them using the existing data. A recent exciting development is the application of ideas from particle theory to cosmology, the physics of the early universe, and the realization that cosmological data are becoming precise enough to constrain the structure of BSM physics. The group has strong links with Jodrell Bank's Theoretical Astrophysics and Cosmology Group for research in this direction.

Theme: Particle Physics - Theory | Supervisor: Christoph Englert

The Large Hadron Collider (LHC) is colliding protons at unprecedented energies in an exciting effort to learn more about the fundamental particles of Nature. After the Higgs discovery at the LHC, the particle physics community is pursuing a gigantic effort of determining the properties of the Higgs boson and hunting for signs of new phenomena beyond our current theoretical understanding of particle physics, the so-called Standard Model (SM). The LHC is searching for undiscovered particles and measuring the interactions of all known particles. If new particles are too heavy to be directly produced in the collisions, their effects can be detected by small modifications of the interactions of the particles that we already know exist. These small modifications can be studied within a theoretical framework that particle physicists call the SM Effective Field Theory (SMEFT). A precise determination of the interactions of the Higgs and all fundamental particles constitutes a challenge, and requires collaboration between experimental and theoretical particle physicists. My work aims at providing accurate theoretical predictions and the necessary computer codes to compute the probabilities of scattering processes occurring at the LHC within the SMEFT. Combining the predictions and data, I will then extract information on the interactions of the elementary particles such as the Higgs boson to other particles and itself. Any modification of interactions found will point to the mass scale of new particles and can provide hints to the answers of the most fundamental questions of Nature.

Theme: Particle Physics - Theory | Supervisor: Michael Seymour

In high energy physics we are usually interested in interactions between partons (quarks and gluons) with high momentum transfer, producing new particles like the Higgs boson or supersymmetric partners, or more familiar ones like the top quark. These decay to produce further partons. However, partons cannot propagate freely but are confined into hadrons, the particles that interact with the detectors around the collision region. This process by which a few hard partons evolve into a system of hundreds of hadrons is far too complicated to calculate analytically and must be modelled numerically, with Monte Carlo techniques. Any attempt to understand the data from the LHC or other high energy collider experiments would be completely impossible without Monte Carlo event generators that simulate them.

Professor Seymour is a senior author of Herwig, one of the three general purpose event generators used by the LHC experiments. He is currently working on theoretical projects to improve the formal accuracy of the approximations used in event generators, called parton shower algorithms, and on more phenomenological projects, to use current data to validate and tune the modelling in the event generators to provide LHC predictions with quantified accuracy. He also works closely with experimenters using event generators to optimize their analyses and get the maximum value out of their data.

Theme: Particle Physics - Theory | Supervisor: Thomas Cridge

A key ingredient for the precise theoretical prediction of parton collisions at colliders, such as the LHC, is knowledge of proton structure. This is encoded in Parton Distribution Functions (PDFs) which describe the energy and longitudinal momentum dependence of the quarks and gluons inside the proton. The question of proton structure at high energies is therefore both an interesting theoretical one, but also of vital experimental importance, acting as both a key input and output of the vast majority of analyses at the LHC and beyond. Their precision also limits the determination of key parameters of the Standard Model such as the strong coupling constant of QCD. These PDFs are determined by combining the highest order QCD predictions with the latest precision LHC data. Members of our group are world-leading in this regard, leading the small UK-based MSHT PDF collaboration. PhD projects in this area will therefore involve joining our small pre-existing team of world experts to combine precision theoretical predictions and developments on theoretical uncertainties with the latest LHC data. The work is therefore phenomenological in nature, and will involve both analytic and computational aspects, depending on the preference of the candidate the project can be tailored somewhat however in its topic and methodology. Through this work we seek to maximise the impact of the LHC and precision QCD to improve our understanding of particle physics.

Theme: Particle Physics - Theory | Supervisor: Peter Millington

One of the most powerful mathematical frameworks that we have for describing the subatomic building blocks of nature (the elementary particles) and the forces that act between them is called quantum field theory. Given the many successes of the Standard Model of particle physics, it might come as a surprise that there remain many important and outstanding questions in quantum field theory itself, with implications for a wide range of areas, from high energy physics, cosmology, astroparticle physics and gravitation, to condensed matter and solid state physics.

We are working on various aspects of quantum field theory and its applications across fundamental physics, and examples include:

• Revisiting basic principles in quantum theory, such as the condition of Hermiticity of the Hamiltonian, which can be relaxed in favour of other discrete anti-linear symmetries in the framework of pseudo-Hermitian quantum theory, whose extension from quantum mechanics to quantum field theory we are pioneering.

• Constructing frameworks within quantum field theory that can describe the relativistic quantum dynamics of open systems, those at finite temperature, or those evolving out-of-thermodynamic equilibrium.

• Building techniques that go beyond perturbation theory, based, e.g., on the quantum effective action or the functional renormalization group, which allows us to study how physics changes with energy scale.

• Understanding the behaviour of the ground states of quantum field theories, and quantum field theories in curved spacetime, with potential implications for the famous cosmological constant problem and the infra-red divergences that arise in massless gauge theories, such as QED and QCD.

Theme: Particle Physics - Theory | Supervisor: Mrinal Dasgupta

Quantum Chromodynamics (QCD) has been established at collider experiments as the theory of strong interactions, which are responsible for binding elementary quarks and gluons into nucleons. It has emerged that QCD is a remarkable theory with a split personality, possessing a friendly regime where one can do calculations using perturbative techniques (Feynman Graphs) and a more challenging non-perturbative region beyond the control of any methods that derive directly from the QCD Lagrangian,and hence still ill-understood. Additionally, while calculations in QCD perturbation theory are in principle well defined, in practice carrying out such calculations at the level of precision required by most experimental data from particle colliders is also a formidable challenge. Moreover due to the fact that non-perturbative effects are always present, devising techniques to better understand the non-perturbative region is critical to the accurate description of data from colliders such as the LHC. We have played a leading role in developing the current theoretical picture of QCD radiation and non-perturbative effects. Our present focus is on the Large Hadron Collider (LHC) experiments and the search for new physics. Since the LHC collides strongly interacting particles (protons), QCD radiation affects all LHC processes and understanding it in detail is of great importance to enable discoveries of new physics at the TeV scale. Our current research is playing a vital role in bringing a deep understanding of QCD to bear on developing precision tools to hunt for new physics such as supersymmetry, dark matter or extra dimensions, at the LHC.

Theme: Continuum mechanics | Supervisor: Alice Thompson

My research interests are in fluid dynamical systems with deformable interfaces, for example bubbles in very viscous fluid, or inkjet printed droplets. The deformability of the interface can lead to complex nonlinear behaviour, and often occurs in configurations where full numerical simulation of the three-dimensional system is computationally impossible.

This computational difficulty leaves an important role for mathematical modelling, in using asymptotic or physical arguments to devise simpler models which can help us understand underlying physical mechanisms, make testable predictions, and to directly access control problems for active (feedback) or passive control mechanisms.


Most recently I am interested in how different modelling methodologies affect whether models are robust in the forward or control problems. I am also interested in how control-based continuation methods can be used in continuum mechanics to directly observe unstable dynamical behaviour in experiments, even without access to a physical model.

This research combines fluid dynamics, mathematical modelling, computational methods (e.g. with the finite-element library oomph-lib), experiments conducted in the Manchester Centre for Nonlinear Dynamics, control theory and nonlinear dynamics. I would not expect any student to have experience in all these areas and there is scope to shape any project to your interests.

Theme: Continuum mechanics | Supervisor: Chris Johnson

The field of granular materials encompasses a vast range of materials and processes, from the formation of sand dunes on a beach and snow avalanches in the mountains, to the roasting of coffee beans and the manufacture of pharmaceutical tablets. The science of granular materials is still in its relative infancy, and many aspects of flowing grains cannot yet be predicted with a continuum rheology. Insights into granular material behaviour come from a range of methods, and my research therefore combines mathematical modelling, computation, and laboratory experiments, undertaken at the Manchester Centre for Nonlinear Dynamics laboratories.

Some example areas of work suitable for a PhD project include:

- Debris flows and their deposits
Debris flows are rapid avalanches of rock and water, which are triggered on mountainsides when erodible sediment is destabilised by heavy rainfall or snowmelt. These flows cause loss of life and infrastructure across the world, but many of the physical mechanisms underlying their motion remain poorly understood. Because it is difficult to predict where and when a debris flow will occur, scientific observations are rarely made on an active flow. More often, all we have to work from is the deposit left behind, and some detective work is required to infer properties of the flow (such as its speed and composition) from this deposit. This project focuses on developing theoretical models for debris flows that predict both a debris flow and its deposit -- in particular the way in which grains of different sizes are distributed throughout the deposit. The aim is then to invert such models, allowing observations of a deposit, when combined with model simulations, to constrain what must have happened during the flow.

- Modelling polydispersity
Much of the current theory of granular materials has been formulated with the assumption of a single type of grain. When grains vary in size, shape or density, it opens up the possibility that such grains with different properties separate from one another, a process called segregation. A fundamental question in this area is predicting the rate of segregation from a description of a granular material, such as the distribution of particle sizes. Thanks to some recent developments, we are approaching a point where this can be done for very simple granular materials (in particular those containing only two, similar, sizes sizes of grain), but many practical granular materials are much more complex. For example, it is common for mixtures of grains used in industry to vary in diameter by a factor of more than 100, and the complex segregation that can occur in these mixtures is poorly understood. This project will make measurements of the segregation behaviour of such mixtures and use these to put together a theoretical framework for describing segregation in complex granular materials.

Theme: Continuum mechanics | Supervisor: Joel Daou

Several projects are available related to the mathematical theory of flame propagation, non-isothermal reactive flows, and combustion instabilities-a fascinating multidisciplinary area of applied mathematics involving ordinary and partial differential equations. Combustion basics will be introduced to the candidate as needed. The approach will typically combine analytical techniques (asymptotic methods) and/or numerical techniques (solutions of ODEs or PDEs).

The multidisciplinary experience gained in combustion and non-isothermal reactive flows will be valuable for tackling research problems in other application fields and will constitute a strong asset for careers in industry (such as the automobile or aeronautics sectors).

Depending on the candidate's interests, each project can be tailored in scope and methodology. Suggested sample projects include:

• Propagation and Coupled Hydrodynamic Front Instabilities under Confinement:
This project investigates the hydrodynamic instabilities of propagating interfaces in Hele-Shaw cells and porous media. The research focuses on an interface between two fluids subject to the coupled Darrieus-Landau, Saffman-Taylor, and Rayleigh-Taylor instabilities. Building on a recent unifying theory, the project will employ theoretical analysis and advanced numerical simulations to explore the linear and nonlinear development of these instabilities. The ultimate goal is to gain fundamental insights and formulate effective control strategies for interface stability in confined geometries.

• Taylor Dispersion in Premixed Combustion:
In 1953, the British physicist G. I. Taylor published an influential paper describing the enhancement of diffusion processes by shear flow, now known as Taylor dispersion. This phenomenon has since generated thousands of publications in transport theory, yet surprisingly none in combustion. In 1940, the German chemist G. Damköhler postulated two hypotheses that have profoundly shaped modern views on premixed-flame propagation in turbulent flows. This project consists of pioneering investigations linking Taylor dispersion and Damköhler's hypotheses, and is expected to provide significant new insight into turbulent combustion.

• Laminar Aspects of Turbulent Combustion:
The idea is to ask whether fundamental questions of turbulent combustion can be answered in simple laminar flows. Since the answer is often no, this project will formulate and study appropriately simplified problems in laminar-flow configurations to shed light on these fundamental questions.

• Generalised Flame Balls and Their Stability:
Flame balls-spherical regions of burnt gas in a reactive mixture-constitute stationary solutions of nonlinear Poisson equations. First described by the Russian physicist Zeldovich about 70 years ago, these solutions are typically unstable, providing a powerful ignition criterion that determines the minimum spark energy required to generate propagating flames. Several projects are available to extend the study of these structures (their existence and stability) to account for realistic effects such as flow fields, mixture non-uniformity, and proximity of walls.

• Flame Initiation and Propagation in Spatially Non-Uniform Mixtures:
This problem is of considerable interest whenever reactants are spatially separated. The project will be based on asymptotic and/or numerical methods. The combustion fundamentals needed for the work will be provided and explained to the candidate.

Theme: Continuum mechanics | Supervisor: Nico Gray, Chris Johnson

Debris flows, snow avalanches and pyroclastic flows are all examples of what are known as geophysical mass flows. These are complex mixtures of rock, water, wood, ice and hot gases that avalanche down slopes under the action of gravity, and pose a direct threat to many communities throughout the world, as well as the infrastructure that they rely on. Although you may think the physics of these flows is very different, they share many common features. In particular, they can all spontaneously (i) develop large-amplitude fast-moving surge waves that concentrate their destructive potential, and (ii) form static levees that confine the flow laterally and enhance overall run out. Our group in Manchester is at the forefront of developing new depth-averaged mixture models to describe how the different material components are transported by these flows. For instance, in the case of debris flows, particle-size segregation allows large rocks and boulders to rise towards the flow surface, while finer particles percolate down towards the base. This vertical structure leads to differential transport of the two species, because the upper layer of the avalanche moves down slope faster than the base. Large rocks and boulders are therefore preferentially transported to flow fronts, where they can accumulate, and generate large impact pressure on structures. Similarly, vertical structure and shear effects between the water and the grains can also lead to the fronts being drier and more granular. The ability to form drier/bouldery fronts retards the flow, which is either pushed along by the more mobile material behind, or the rocks and boulders are pushed aside to form static confining levees. As mathematicians, we gain physical insight by working closely with field monitoring groups in Switzerland and the USA, and by performing our own small-scale analogue experiments in our laboratory in Manchester. The knowledge we gain from this is vital in deriving new theoretical models that can capture the essential missing physics. As well as developing new theories, we also develop time-dependent numerical methods to solve the resulting partial differential equations, and exact or approximate solutions that provide significant insights, e.g., into what sets the height and width of a self-channelized flow? There are many open questions in this area. In particular, due to climate change the nature of the hazards is also changing. For instance, the occurrence of debris flows seems to be intensifying in response to increased rainfall intensity, and the melting of permafrost, while slower moving wet-snow avalanches that form huge levees are becoming more prevalent. Individual PhD projects are flexible and are likely to focus on a specific type of geophysical mass flow.

Theme: Continuum mechanics | Supervisor: William Parnell

Complex materials are important in almost every aspect of our lives, whether that is using a cell phone, insulating a house, ensuring that transport is environmentally friendly or that packaging is sustainable. An important facet of this is to ensure that materials are optimal in some sense. This could be an optimal stiffness for a given weight or an optimal conductivity for a given stiffness. Foams are an important class of material that are lightweight but also have the potential for unprecedented mechanical properties by adding nano-reinforcements (graphene flakes or carbon nanotubes) into the background or matrix material from which the foam is fabricated. When coupled with experimentation such as imaging and mechanical testing, mathematical models allow us to understand how to improve the design and properties of such foams.

A number of projects are available in this broad area and interested parties can discuss these by making contact with the supervisor.

Theme: Continuum mechanics | Supervisor: William Parnell

The ability to control electromagnetic waves, sound, vibration has been of practical interest for decades. Over the last century a number of materials have been designed to assist with the attenuation of unwanted noise and vibration. However, recently there has been an explosion of interest in the topic of metamaterials and metasurfaces. Such media have special microstructures, designed to provide overall (dynamic) material properties that natural materials can never hope to attain and lead to the potential of negative refraction, wave redirection and the holy grail of cloaking. Many of the mechanisms to create these artificial materials rely on low frequency resonance. Frequently we are interested in the notion of homogenisation of these microstructures and this requires a mathematical framework.
A number of projects are available in this broad area and interested parties can discuss these by making contact with the supervisor.

Theme: Continuum mechanics | Supervisor: Raphael Assier

Several projects are available to explore the connections between waves and multidimensional complex analysis. These will be supervised by me, Raphael Assier, within the Department of Mathematics of the University of Manchester.

By waves, here I refer to 2D or 3D solutions to either the linear wave equation or the Helmholtz equation. These occur naturally in acoustics, electro-magnetism, elasticity and water waves for instance and are crucial in a myriad of important applications. Functions of several complex variables occur very naturally in wave theory through double or triple Fourier transform of the wave or Helmholtz equation. I am particularly interested in two specific areas of wave theory:

- Wave diffraction by sharp edges and corners
- Wave propagation within periodic media, and links to the concept of metamaterials.

Both areas are very active from a research point of view and are linked to a vibrant community within the UK and beyond.

Multidimensional complex analysis (the study of functions that depend on several complex variables) has mostly been studied by pure mathematicians and its main results are largely unexploited in applied mathematics. However, over the past six years, together with my collaborators, I have laid the foundations for a wider application of multidimensional complex analysis in wave theory.

The idea behind this project is to bring together ideas from partial differential equations, topology, algebraic geometry, asymptotics, approximation theory, analytical continuation, singularity theory and Fourier analysis to tackle unsolved problems in wave theory.

This should appeal to candidates who have a strong interest in both applied and pure mathematics. Each of the projects will naturally be tailored to the interests and skillset of the candidate.

Suggested sample projects include (but are not limited to):

- Working on open canonical diffraction problems such as the 3D quarter-plane problem (see e.g. [1, 2, 3, 4]) or the 2D penetrable wedge problem (see e.g. [5, 6, 7, 8]).
- Formal study (either asymptotically or numerically) of singular and oscillatory multiple integrals, see [9].
- Numerical/Analytical resolution of functional equations in two (or more) complex variables (see e.g. [2, 5]).
- Studying degeneracies and Green's functions in periodic media (see e.g. [10])

Funding is available for these projects, though it is subject to a competitive process within the Department of Mathematics at the University of Manchester. Successful candidate(s) would then be joining the vibrant and diverse Mathematics of Waves and Materials (MWM) research group. Have a look at our website (https://www.mwmresearchgroup.org) or at my personal website (https://raphaelassier.weebly.com/).

Selected References:
[1] R.C. Assier and A.V. Shanin (2018) Q. Jl. Mech. Appl. Math. 72 (1):51-86
[2] R.C. Assier and I.D. Abrahams (2021) SIAM J. Appl. Math. 81(1), 60-90
[3] R.C. Assier and A.V. Shanin (2021) Q.J. Mech. Appl. Math., 74(3):251-295
[4] R.C. Assier, A.V. Shanin and A. I. Korolkov (2024) Q. J. Mech. Appl. Math., 77(1-2): hbae005
[5] V.D. Kunz and R.C. Assier (2022) SIAM J. Appl. Math. 82(4), 1495-1519
[6] V.D. Kunz and R.C. Assier (2023) Q. J. Mech. Appl. Math., 76(2):211-241
[7] V.D. Kunz and R.C. Assier (2024) IMA J. Appl. Math. 89(3):463-497
[8] M. Nethercote, R.C. Assier and I.D. Abrahams (2020) IMA J. Appl. Math. 85(3):421-466
[9] R.C. Assier, A.V. Shanin, A.I. Korolkov (2022) Q. J. Mech. Appl. Math., 76(1):1-47
[10] A.V. Shanin, R.C. Assier, A.I. Korolkov, O.I. Makarov (2024) Phys. Rev. B. 110, 024310

Theme: Mathematics in the life sciences | Supervisor: Oliver Jensen

Biological tissues have an intrinsically multiscale structure. They contain components that range in size from individual molecules to the scale of whole organs. The organisation of individual components of a tissue, which often has a stochastic component, is intimately connected to biological function. Examples include exchange organs such as the lung and placenta, and developing multicellular tissues where mechanical forces play an crucial role in growth. To describe such materials mathematically, new multiscale approaches are needed that retain essential elements of tissue organisation at small scales, while providing tractable descriptions of function at larger scales. Projects are available in these areas that offer opportunities to collaborate with life scientists while developing original mathematical models relating tissue structure to its biological function.

Theme: Numerical analysis and scientific computing | Supervisor: David Silvester

I would be happy to supervise projects in the general area of efficient solution of elliptic and parabolic partial differential equations using finite elements. PhD projects would involve a mix of theoretical analysis and the development of proof-of-concept software written in MATLAB or Python. The design of robust and efficient error estimators is an open problem in computational fluid dynamics.

Recent papers on this topic include

Alex Bespalov, Leonardo Rocchi and David Silvester, T--IFISS: a toolbox for adaptive FEM computation, Computers and Mathematics with Applications, 81: 373--390, 2021.
https://doi.org/10.1016/j.camwa.2020.03.005

Arbaz Khan, Catherine Powell and David Silvester, Robust a posteriori error estimators for mixed approximation of nearly incompressible elasticity, International Journal for Numerical Methods in Engineering, 119: 1--20, 2019.
https://doi.org/10.1002/nme.6040

John Pearson, Jen Pestana and David Silvester, Refined saddle-point preconditioners for discretized Stokes problems, Numerische Mathematik, 138: 331--363, 2018.
https://doi.org/10.1007/s00211-017-0908-4

Theme: Numerical analysis and scientific computing | Supervisor: David Silvester

I would be happy to supervise projects in the general area of efficient solution of elliptic and parabolic partial differential equations with random data. PhD projects would involve a mix of theoretical analysis and the development of proof-of-concept software written in MATLAB or Python. The design of robust and efficient error estimators for stochastic collocation approximation methods is an active area of research within the uncertainty quantification community.


Recent papers on this topic include

Alex Bespalov, David Silvester and Feng Xu. Error estimation and adaptivity for stochastic collocation finite elements Part I: single-level approximation, SIAM J. Scientific Computing, 44: A3393--A3412, 2022.
https://doi.org/10.1137/21M1446745

Arbaz Khan, Alex Bespalov, Catherine Powell and David Silvester, Robust a posteriori error estimators for stochastic Galerkin formulations of parameter-dependent linear elasticity equations, Mathematics of Computation, 90: 613--636, 2021.
https://doi.org/10.1090/mcom/3572

Jens Lang, Rob Scheichl and David Silvester, A fully adaptive multilevel collocation strategy for solving elliptic PDEs with random data, J. Computational Physics, 419, 109692, 2020.
https://doi.org/10.1016/j.jcp.2020.109692

Theme: Numerical analysis and scientific computing | Supervisor: Anthony Thornton

I welcome applications from students interested in developing cutting-edge mathematical and computational tools for simulating and optimising the behaviour of granular materials - mixtures of particles such as powders, grains, and aggregates. These materials are central to industries including pharmaceuticals, food processing, and construction, yet their behaviour remains notoriously difficult to predict. By advancing virtual prototyping techniques, this research area aims to reduce the need for expensive and wasteful physical trials and to enable the rational design of efficient, sustainable industrial processes.

The work sits at the interface of applied mathematics, scientific computing, and engineering. Depending on your interests and background, you may develop new open-source numerical methods using continuum modelling in oomph-lib, discrete particle simulations in MercuryDPM, or multiscale and/or multiphysics approaches that combine both. The associated mathematical challenges include formulating, analysing, and solving models that bridge individual particle interactions with continuum-level behaviour. A central theme is the "calibration problem": determining material and model parameters from experimental or simulation data. There is also scope to incorporate modern machine-learning methods to build robust, data-driven parameter-estimation and uncertainty-quantification frameworks.

Students interested in computational efficiency may explore reduced-order models (ROMs) using tools such as pyMOR. These ROMs aim to preserve the essential mathematical structure of high-fidelity models while greatly reducing computational cost, enabling rapid simulation and optimisation of large-scale systems. Such ROMs can ultimately be integrated into oomph-lib to support advanced workflows for the design and improvement of mixing, blending, and segregation processes.

I am open to PhD projects across all of these themes. This research area offers excellent opportunities for students with interests in PDEs, numerical analysis, model reduction, machine learning for physical systems, or scientific software development. It combines deep mathematical questions with tangible industrial impact, and all methods developed contribute to the wider open-source scientific computing ecosystem. Applicants from a broad range of applied mathematics backgrounds are encouraged to apply.

Theme: Numerical analysis and scientific computing | Supervisor: Yoshihito Kazashi

High-dimensional computations are ubiquitous in science and engineering, often arising from models with numerous parameters. For instance, uncertainty quantification (UQ) in fields such as climate modelling, nuclear reactor design, and finance often involves models with thousands of variables, posing significant mathematical challenges.

A range of projects are available to address these challenges. Our aim is to develop and analyse implementable, fully discrete methods for function approximation, density estimation, and/or time-dependent PDEs or SDEs in high dimensions, with links to UQ and theoretical aspects of machine learning. Applications include improving the efficiency of data assimilation methods and understanding why and how deep learning works.

Depending on the project, applicants should be familiar with at least one, and preferably two, of:
(a) numerical analysis and real or elementary functional analysis;
(b) probability theory;
(c) implementation of computational methods using, for example, Julia or Python.

Recent papers on this topic include:

Kazashi, Y., Suzuki, Y., & Goda, T. (2025). Optimality of quasi-Monte Carlo methods and suboptimality of the sparse-grid Gauss--Hermite rule in Gaussian Sobolev spaces. arXiv:2509.18712.

Kaarnioja, V., Kazashi, Y., Kuo, F. Y., Nobile, F., & Sloan, I. H. (2022). Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification. Numerische Mathematik, 150(1), 33-77.

Kazashi, Y., & Nobile, F. (2023). Density estimation in RKHS with application to Korobov spaces in high dimensions. SIAM Journal on Numerical Analysis, 61(2), 1080-1102.

Kazashi, Y., Nobile, F., & Zoccolan, F. (2025). Dynamical low-rank approximation for stochastic differential equations. Mathematics of Computation, 94(353), 1335-1375.

Theme: Numerical analysis and scientific computing | Supervisor: Catherine Powell

Scientific Machine learning (SciML) and AI methods are becoming increasingly popular as data-driven approaches to building surrogates for physical models such as partial differential equations (PDEs). While they offer more flexibility in how data can be incorporated into the simulation process, standard approaches often ignore, or are not able to enforce important structural information. For example, in fluid flow modelling, we often require velocity approximations to be mass-conserving. In structural engineering problems, approximations may need to have specific spatial structures due to geometric constraints. While there has been some research that attempts to incorporate this information into an AI model, these have had limited success for complex and nonlinear problems compared to bespoke adaptive numerical methods derived using rigorous numerical analysis arguments. Finding novel ways to fuse structural and other domain-specific information, where it exists, with data holds the promise to not only produce better ML/AI models that are easier to fit but also more robust approximations that have smaller generalisation error. In projects in this area, students will develop connections between numerical analysis of, and numerical methods for differential equations and the design and analysis of novel SciML methods. Possible project topics include:
• Physics-reinforced machine learning methods
• Developing hybrid classical and data-driven solvers for PDEs/parametric PDEs
• Designing neural network architectures that mimic structure-preserving numerical schemes
• Using ML tools to learn parameters to optimise performance of classical numerical methods

Suitable applicants must have a background in some aspect of numerical analysis, and some programming experience, for example in MATLAB or Python.

Theme: Numerical analysis and scientific computing | Supervisor: Catherine Powell

In applied mathematics, we model physical processes in the world around us (heat transfer, fluid flows, deformation of elastic bodies), using partial differential equations (PDEs). For many PDEs, state of the art numerical methods (eg finite element methods) discretise the problem in space and time, leading to large structured linear systems that can be time consuming to solve.

Uncertain inputs in PDE models, such as material coefficients, boundary conditions and/or parameters associated with geometry can be represented mathematically as random variables. Such models are often called parametric PDEs. Naive sampling methods (eg Monte Carlo) require the repeated solution of the PDE model for multiple samples of the inputs drawn from an appropriate probability distribution. When the cost of solving the PDE for just one sample takes minutes to hours of computation time, obtaining accurate uncertainty assessments becomes highly problematic. A possibly remedy is to build a surrogate.

A surrogate model is an approximation that can be quickly evaluated to give an approximation of the solution of a parametric PDE for new parameters of interest without having to re-solve the PDE. Constructing surrogates with cast iron accuracy guarantees is, however, extremely challenging.

Nowadays, a wide range of such approaches are available, from polynomial-based methods, reduced basis methods, statistical emulators, operator learning and other data-driven machine learning techniques. A range of projects are available in this area, but suitable applicants must have a background in numerical analysis, and some programming experience, for example in MATLAB or Python.

Theme: Probability, financial mathematics and actuarial science | Supervisor: Paul Johnson, Huy Chau

Financial decision-making under uncertainty is fundamentally a problem of optimal control. This PhD project will develop and analyse advanced numerical methods for solving such problems, which lie at the intersection of applied mathematics, probability, and computational finance. We will explore a range of problems, from the optimal timing of a single investment (optimal stopping) to the continuous rebalancing of a portfolio (stochastic control). The core challenge is to efficiently solve the associated Hamilton-Jacobi-Bellman (HJB) partial differential equations or their backward stochastic differential equation (BSDE) counterparts, which are often high-dimensional, non-linear, and plagued by the curse of dimensionality.

The project will undertake a rigorous comparative analysis of three numerical approaches: PDE-based methods (in particular finite difference), Monte Carlo simulation techniques, and machine learning. PDE methods offer high accuracy for low-dimensional problems but struggle with scalability. Monte Carlo methods, excel in higher dimensions but can suffer from noise and high computational cost. Emerging machine learning techniques promise to break through traditional dimensionality barriers. A key objective is to critically contrast these methods, and to develop novel hybrid algorithms that leverage the best aspects of each.

The numerical frameworks will be applied to small selection of financially relevant models, before focussing on one in particular. This might include portfolio optimisation and exotic option pricing, where the underlying processes are standard financial assets. Another avenue to investigate could be models involving physical assets or real options, such as the valuation of energy infrastructure, natural resource extraction, or technology adoption.

The successful candidate will join a vibrant research environment with joint supervision from the applied mathematics group and probability group. There is an expectation that the student already has a solid foundation in PDEs, probability and finance, and is familiar with numerical methods.

Theme: Statistics, inverse problems, uncertainty quantification and data science | Supervisor: Simon Cotter

A range of projects are available on the topic of statistical inverse problems, in particular with application to problems in applied mathematics. Our aim is to construct new methods for the solution of statistical inverse problems, and to apply them to real problems from science, biology, engineering, etc. These may be more traditional Markov chain Monte Carlo (MCMC) methods, Piecewise-deterministic Markov processes (PDMPs), gradient flows (e.g. Stein gradient descent), or entirely new families of methods. Where possible the methods will be flexible and widely applicable, which will enable us to also apply them to real problems and datasets.

Some recent applications involve cell matching in biology, and characterisation of physical properties of materials, for example the thermal properties of a manmade material, or the Young's modulus of a tendon or artery.

The project will require the candidate to be proficient in a modern programming language (e.g. Python).

Theme: Statistics, inverse problems, uncertainty quantification and data science | Supervisor: Catherine Powell

In applied mathematics, we model physical processes in the world around us (heat transfer, fluid flows, deformation of elastic bodies), using partial differential equations (PDEs). For many PDEs, state of the art numerical methods (eg finite element methods) discretise the problem in space and time, leading to large structured linear systems that can be time consuming to solve.

In forward uncertainty quantification (UQ), we aim to understand how uncertainty in model inputs affects predictions of quantities of interest related to model solutions. For example, think about predicting the temperature in an engine component when we are uncertain about the material it is made from, or its operating conditions. Uncertain inputs in PDE models, such as material coefficients, boundary conditions and/or parameters associated with geometry can be represented mathematically as random variables. Such models are often called parametric PDEs.

Naive sampling methods (eg Monte Carlo) require the repeated solution of the PDE model for multiple samples of the inputs drawn from an appropriate probability distribution. When the cost of solving the PDE for just one sample takes minutes to hours of computation time, obtaining accurate uncertainty assessments becomes highly problematic. A possibly remedy is to build a surrogate model.

A surrogate model is an approximation that can be quickly evaluated to give an approximation of the solution of a parametric PDE for new parameters of interest without having to re-solve the PDE. Nowadays, a wide range of such approaches are available, from polynomial-based methods, reduced basis methods, statistical emulators, operator learning and other data-driven machine learning techniques.

A range of projects are available in this area, but suitable applicants must have a background in numerical analysis, and some programming experience, for example in MATLAB or Python.

Theme: Statistics, inverse problems, uncertainty quantification and data science | Supervisor: Jonas Latz

Machine learning and artificial intelligence play a major part in our everyday life. Self-driving cars, automatic diagnoses from medical images, face recognition, or fraud detection, all profit especially from the universal applicability of deep neural networks. Their use in safety critical applications, however, is problematic: no interpretability, missing mathematical guarantees for network or learning process, and no quantification of the uncertainties in the neural network output.

Recently, models that are based on partial differential equations (PDEs) have gained popularity in machine learning. In a classification problem, for instance, a PDE is constructed whose solution correctly classifies the training data and gives a suitable model to classify unlabelled feature vectors. In practice, feature vectors tend to be high dimensional and the natural space on which they live tends to have a complicated geometry. Therefore, partial differential equations on graphs are particularly suitable and popular. The resulting models are interpretable, mathematically well-understood, and uncertainty quantification is possible. In addition, they can be employed in a semi-supervised fashion, making them highly applicable in small data settings.

I am interested in various mathematical, statistical, and computational aspects of PDE-based machine learning. Many of those aspects translate easily into PhD projects; examples are
- Efficient algorithms for p-Laplacian-based regression and clustering
- Bayesian identification of graphs from flow data
- PDEs on random graphs
- Deeply learned PDEs in data science

Depending on the project, applicants should be familiar with at least one of: (a) numerical analysis and numerical linear algebra; (b) probability theory and statistics; (c) machine learning and deep learning.

Theme: Atomic and Photon Physics | Supervisor: Andrew Murray

Our research combines electron and laser interactions with atomic and molecular targets to study the fundamental processes that lead to excitation and ionization. This research is important in fields ranging from understanding energy loss mechanisms in Tokomaks, through to studying how low-energy electrons cause DNA breaks in cells leading to cancer. We combine high-resolution laser and electron beams to probe these interactions. Laser beams are used to cool, trap and excite atoms before an electron beam further excites, de-excites or ionizes the target under study. In this way we precisely control their quantum state, with the results from our measurements being compared to models developed by colleagues in Europe, the USA, Australia and the UK. We are the leading group in the world in this area of research, with experiments conducted using custom-built spectrometers together with the laser facilities in the Photon Science Institute. We operate experiments that study electron-impact excitation and ionization from laser-excited atoms and molecules, the production of cold electrons from cold atoms, and the production and study of highly excited neutral Rydberg atoms (whose diameters are up to 10% that of a human hair).

Research projects include:
• Electron impact ionization and excitation of atoms and molecules.
• Study of quantum interference from two-colour photoionization pathways using a toroidal spectrometer (a 'double-slit' experiment with a single atom - see Physics World, Feb 2020) (fully funded EPSRC project).
• Production of a quantum diffraction grating using single photo-electrons emitted from a cold atom array (fully funded EPSRC project).
• Producing & ionizing highly excited Rydberg atoms following stepwise electron impact and laser excitation (fully funded EPSRC project).

Theme: Atomic and Photon Physics | Supervisor: David Binks

LEDs based on InGaN/GaN quantum wells are revolutionising the efficiency of lighting, leading to a significant reduction in global power consumption and consequent impact on the environment. However, while these LEDs work well in the blue spectral region, they are much less efficient at other wavelengths. This necessitates the combination of a blue LED with a yellow phosphor to produce light that is sufficiently 'white' for the illumination of homes and offices, even though this involves an inherent energy loss. A much more efficient and controllable approach would be to make white light by combining the output of different coloured LEDs.

One reason why InGaN/GaN quantum wells become less efficient for emission at longer wavelengths is that obtaining LEDs that emit at these colours involves increasing the indium concentration in the quantum wells. This results in a stronger electric field across the well separates the electron and hole wavefunctions, reducing the rate at which they recombine radiatively so that it is less competitive with non-radiative processes. This electric field largely originates as a consequence of the hexagonal crystal phase of typical InGaN/GaN quantum wells.
Currently we are investigating carrier recombination processes in GaN films and InGaN/GaN quantum wells grown in the cubic crystal phase, the greater crystal symmetry of which greatly reduces the field across the quantum well. This work is in collaboration with the Department of Materials and Metallurgy at the University of Cambridge. We use a suite of spectroscopic techniques on cryogenically cooled samples in well-equipped, established laboratories. Photoluminescence (PL) and PL excitation spectroscopies are used to determine how carrier recombination is affected by the structure and composition of the samples, with PL decay measurements used to measure the characteristic lifetimes of the underlying processes. Raman spectroscopy is also an important technique because it yields insight in the crystal structure purity of the samples.

Research projects include:
• Investigating the cubic phase of GaN films and InGaN/GaN Quantum Wells.

Theme: Atomic and Photon Physics | Supervisor: Patrick Parkinson

It is over 60 years since Richard Feynman claimed, "There's plenty of room at the bottom", establishing the field of functional nanotechnology. In this field, performance depends on both the geometry and quality of a material. Optical nanotechnology is rapidly emerging as an enabling technology for the new field of on-chip photonic integrated circuitry, which provides a novel alternative for fast, low cost and energy efficiency computation. Key elements include light emitters, lasers, and sensor which must be designed and produced at the sub-wavelength scale; by exploiting advances in bottom-up fabrication, billions of single element devices can be produced in a single growth run. However, understanding the complex behaviour of material, electronics, and light within sub-micron and heterogeneous materials presents a huge challenge. This is particularly the case for photonic quantum technologies, where single photon emitters and detectors must be produced at scale and at high yield.

As part of a multi-million-pound, multi-year UKRI Future Leaders Fellowship "Big-Data for Nano-Electronics", our group develop an experimental and data-science framework for high-throughput functional characterisation of single-element nanotechnology. The aim of this project is to make use of existing high-throughput imaging and spectroscopy tools to measure geometrical and material properties of large ensembles (~106) of single devices which make use of a newly installed cutting-edge laser system. Statistical approaches including Bayesian optimization and machine-learning will be used to identify routes to control and harness disorder, to produce a framework for analysis of large, correlated datasets.

Research projects include:
• Ultra-high-throughput spectroscopy and imaging to the million-endpoint regime.
• Bayesian optimization for model development in nanoelectronics.
• Single-photons and large-scale analysis; joining big-data to quantum measurements.

Theme: Atomic and Photon Physics | Supervisor: Mark Dickinson, Andrea Murray

There is a long standing collaboration between the Photon Physics Research group at the University of Manchester and Salford Royal NHS trust, looking at mainly optical techniques for investigating Systemic Sclerosis (SSc) and Raynaud's phenomenon. Both of these conditions affect the microcirculation of the peripheral limbs, and we have been using these techniques as a window into the disease diagnosis and progression. It is anticipated that some of the projects will involve collaboration with industrial partners and may lead to CASE awards.

Research projects include:
• Advanced imaging (such as photo-acoustics).
• Using mobile devices for patient self-monitoring of disease progression.
• Functional imaging of the microvasculature using our techniques as an adjunct to MRI, microCT and biopsy.

Theme: Atomic and Photon Physics | Supervisor: Darren Graham

Terahertz radiation, which sits between infrared and microwave radiation on the electromagnetic spectrum has historically been very difficult to utilise, and yet this last unexplored region of the spectrum has the potential to transform a diverse range of fields. My group's research interests are focused primarily on the development and exploitation of novel terahertz radiation sources. I address challenges both within the fields of photon physics and accelerator physics. Within the field of photon physics, my group uses ultrafast laser spectroscopic techniques to develop novel sources of terahertz (THz) radiation utilising the state-of-the-art laser facilities at the Photon Science Institute (PSI), and working closely with industrial partners.

PhD projects include (but not limited to):

• Ultrafast Spintronics - Recently, the emission of extremely broadband electromagnetic radiation, spanning from the mid- to far-infrared spectral regime and covering the so- called 'terahertz gap' in the spectrum, from ferromagnetic structures has led to an exciting new route for the generation of terahertz radiation. The ability to control the properties of the emitted THz radiation also has the potential to facilitate a wide range of diverse, technologically demanding scientific applications, from improved medical diagnosis to non-destructive testing and advanced airport security scanners. Furthermore, by understanding the fundamental emission process we will be able to establish new characterisation tools for use in developing the next generation of spintronic devices, where ultrafast spin processes are being investigated for data storage and manipulation.

• Ultrafast Terahertz Spectroscopy of GaN Semiconductor Structures - The 2014 Nobel prize in Physics was awarded for the invention of the efficient blue light-emitting diodes (LEDs) that have enabled the development of bright and energy-saving white light sources. This breakthrough in the blue part of the spectrum has spurred interest around the world in exploiting GaN semiconductor quantum wells, the material at the heart of blue LEDs, in other regions of the electromagnetic spectrum. One region of particular interest is the terahertz region. To realise the potential of this region we require compact, efficiency and powerful sources of terahertz radiation and the fundamental properties of GaN semiconductors make this a tantalising possibility. In this project the student will use the state-of-the-art laser facilities within the Photon Science Institute to reveal the physics that governs the properties of this remarkable materials system and optimise GaN-based quantum well structures for terahertz sources and detectors. This work will be carried out in close collaboration with the Materials Science Department at the University of Cambridge. The opportunity to work in collaboration with international renowned academics will provide training in cutting-edge experimental physics techniques. The skills gained will provide a solid foundation for a future career in industry or academia.

Theme: Biological Physics | Supervisor: J Lu

Neutron reflection study of protein adsorption.
Proteins are large biomacromolecules that perform many functions in living systems. They are folded up from one or several polypeptide chains. In order to perform their functional roles, they must retain their 3D structures. Once exposed to surface or interface, protein molecules tend to adsorb, become deformed and then desorbed. During these interfacial processes of adsorption and desorption, protein molecules undergo different interactions that may damage their 3D structures and deactivate them. Neutron reflection could help determine the structural conformation of an adsorbed protein layer. The information could help us develop biocompatible surfaces and interfaces whilst improving our basic understanding. This project also involves computer modelling and collaboration with scientists at Rutherford Laboratory and industry.

Self-assembly of short peptide amphiphiles and their interactions with biointerfaces.
There are many natural and unnatural amino acids that are polar, apolar and charged. We can design short peptide sequences from these amino acids that resemble conventional surfactants with distinct hydrophilic head and hydrophobic tail moieties. Unlike conventional surfactants, however, the properties of these peptide amphiphiles are strongly influenced by hydrogen bonding. Light scattering, neutron scattering and computer modelling are often used together to help understand how a given set of peptide amphiphiles self-assemble to form a range of nanostructures such as nanorods, nanotubes, nanobelts and larger structures templated from them. Materials assembled from these nanostructures may have distinct mechanical, light, biological and piezoelectric functions.

Interfacial processes underlying antimicrobial actions and biocompatibility.
A distinct mode of antimicrobial action is to kill bacteria by disrupting their membranes, but antibiotics or equivalent must target bacteria very selectively with minimal damage to mammalian cell hosts. We have developed a range of antimicrobial peptides that can selectively bind to bacterial and fungal membranes whilst remaining benign to host cells. In collaboration with colleagues in biology and medicine, we have combined both physical and biological approaches to help understand the key mechanistic processes of antimicrobial.

Theme: Biological Physics | Supervisor: T A Waigh

Super-resolution fluorescence imaging of bacterial biofilms (with Prof. Ian Roberts in Life Sciences).
A super-resolution fluorescence microscope (STORM) will be used to study biofilm formation in bacteria. Bacterial biofilms are a key issue in antibiotic resistance and are therefore a huge problem in modern medicine. Experiments in our laboratory have demonstrated bacteria can use electrical signalling during biofilm formation. Optogenetics methods are also possible to insert voltage sensitive fluorophores into bacteria to observe their activity.

Models for the creation of bacterial biofilms (with Prof. Ian Roberts in Life Sciences).
Statistical models to describe bacterial biofilms will be constructed. These will include ideas from agent based modelling, colloidal hydrodynamics and systems biology. Electrophysiological effects can also be incorporated into models to describe electrical signalling experiments. A range of medically important biofilms will be studied in collaboration with experimental physicists and microbiologists.

Optical coherence tomography to study the fluid mechanics of opaque solutions of DNA (with Dr Mark Dickinson).
Concentrated (opaque) DNA has a number of novel non-linear flow phenomena, such as turbulence at very low Reynolds number. This project will develop new optoelectronics equipment to study fluid mechanics based on optical fibre interferometry. It will then apply the techniques developed to medically important areas of research including the flow behaviour of DNA and bacteria.
Active cell movement in live tissue (with Dr Tom Millard in Life Sciences)
We want to understand how cells move inside complex living tissues and how the physical properties of the surrounding environment affect cell movement. Drosophila embryos are transparent and we will determine how cell motion is influenced by the spatial properties of the surrounding environment. New statistical tools will be developed to characterize the heterogeneous motility of immune cells.

Theme: Biological Physics | Supervisor: H Zhang-

Development of the computer model of the heart for the study of electrical and mechanical dynamics of the heart.

A grand challenge for modern physics is to develop a biophysically detailed and accurate model for predicting the dynamical behaviours of the heart that paves the way leading to predictive life sciences. In collaboration with colleagues in biology and medicine, we aim to develop multi-scale physics models of the heart to investigate its nonlinear dynamics in electrical and mechanical behaviours ranging from molecular to cell and organ levels, by utilising combined skills of physics and high performance parallel computing.

Inverse problem for novel non-invasive technology for diagnosing cardiac arrhythmic origins.
Cardiac arrhythmias are the leading cause of sudden death. Current treatment of cardiac arrhythmias (e.g. atrial fibrillation) involves the use of catheter ablation. However, the success of catheter ablation relies on accurate identification of the cardiac arrhythmic origins, which is challenging at the moment. The aim of this project is to develop a new algorithm that solve the inverse problem of the heart, by which electrical excitation dynamics in the heart can be reconstructed from multi-channel ECG recordings from the human body surface. This will provide a new non-invasive technology for identifying the target for ablation, which will have significant practical values.

Digital twins of the heart as a platform for new drug design and testing.
Cardiac arrhythmias are the leading cause of sudden death. Current treatment of cardiac arrhythmias by using of anti-arrhythmic drugs is unsatisfactory due to the toxic side effect of the drugs. The aim of this project is to develop a novel computer model of the heart for testing the efficacy and safety of the drugs. This will provide a new technology which has great potential application in the drug industry.

Artificial intelligence (AI) in diagnosing cardiac arrhythmias.
AI-based deep machine learning may revolutionise the way of automatic clinical diagnosis. The aim of this project is to develop a new set of AI algorithms that analyse the nonlinear dynamics of heart from multi-channel ECG recordings from the human body surface. This will provide a new technology for accurate diagnosis of cardiac arrhythmias.

Development of AI algorithm for searching for antimicrobial peptides (with Prof. Jian Lu)
Antibiotic resistance has fast become a global healthcare threat over the past two decades. Resistant microorganisms can compromise many antibiotics, making previously effective medical treatments less effective or ineffective. It is imperative to explore new alternatives that work differently from the current mainstream of antibiotics. Some antimicrobial peptides (AMPs) kill microorganisms by disrupting microbial membranes. This process of fast structural damage to the microbial membrane is widely thought to generate the much lower rate of resistance. Currently, thousands of these peptides have been reported. However, in vitro experimental screening of either rational or non-rational libraries is tedious, expensive, and often generates only a few AMP candidates, albeit most of them fail to show the required bioactivities and physicochemical properties for practical applications. In this project, we aim to develop an artificial intelligence algorithm to search for high-activity AMPs based on existing public databases. It is hoped that the outcome of the project will provide an AI-based algorithm for AMP screening, which helps to reduce required experimentation and increase the efficiency of high-activity AMP discovery.

Theme: Biological Physics | Supervisor: Jian Lu, T A Waigh

Self-assembled nanobiomaterials are an important research topic due to their potential in infection control and wound care, gene and cell delivery, biodevices and tissue regeneration. Nanostructures such as nanorods, nanobelts, nanofibers and nanotubes can be readily formed through self-assembly from designed short peptides. A particularly interesting group of these short peptides are those containing cationic charges as they can kill pathogenic microbes by binding to microbial membranes and causing structural disruptions. These antimicrobial peptides (AMPs) usually contain 10-14 natural amino acids and are typically amphiphilic, i.e., containing both hydrophobic and cationically charged portions. Whilst AMP molecules undertake self-assembly whilst binding to different cell membranes, a fundamental challenge lies in understanding how to balance their self-interaction against their membrane binding capacity through sequence design.

Various membrane models, e.g., spread lipid monolayers, supported lipid bilayers and small unilamellar vesicles, have been developed to facilitate measurements from atomic force microscopy, electron microscopy, neutron reflection and scattering to probe structural changes across different membranes before and after AMP attack. In an interdisciplinary environment, you will learn to design AMPs from natural amino acids, to improve their antimicrobial efficacy whilst retaining their biocompatibility to host cells and to combine neutron experiments with computer modelling to visualise in-membrane nanostructuring.

Nanostructures self-assembled from peptides or fabricated from lipids have already shown attractive benefits to drug delivery, but further benefits could be realised by exploiting nanostructuring from the hybrids of short peptides and lipids to form novel hydrogels that provide more effective manipulations to the loading and release of drugs that can alleviate current shortcomings.

Projects are available performing experimental and computational research into design and characterizations of interfacial systems and bulk hydrogels, in a fascinating area of soft matter and biophysics. Investigations range from fundamental questions to studies with direct relevance to practical applications, shaping up clear career paths beyond PhD research. Candidates are encouraged to discuss their preference with the supervisors to define project scope and methodology prior to formal applications.

Suitable candidates would have a background in Physics, Chemistry, Materials, molecular biosciences or equivalent, and a keen interest in undertaking the challenges through interdisciplinary work. We welcome both home and overseas students to apply. Highly qualified candidates will be selected to bid for BBSRC and MRC DTP studentships, President and Dean's award and CSC-UoM award. More details on deadlines and criteria can be found from supervisors.

Theme: Condensed Matter Physics | Supervisor: Radha Boya, Patrick Parkinson, Ashok Keerthi

This project will leverage thermal scanning probe lithography (t-SPL) to pattern 2D materials such as graphene and MoS2 and directly write metal-organic resists for creating optofluidic nanodevices. The direct-write capability of t-SPL on metal-organic resists will be investigated to develop spatially resolved, multi-material heterostructures. By integrating patterned 2D materials with nanofluidic channels, the research aims to develop hybrid systems where light interacts with confined liquids. The project is open-ended with broad potential applications including nanoscale waveguides, plasmonic hotspots for molecular sensing, and photon-driven energy harvesting in fluidic environments. The resulting hybrid systems could advance fields such as single-molecule spectroscopy, optofluidic energy harvesting, or photon-mediated chemical reactions. This interdisciplinary project combines cutting-edge lithography, 2D material science, and photonics to design next-generation nanoscale devices with broad implications for quantum technologies and light-fluid interactions.
Training and research environment:
Research will be experimental and based in Photon Science Institute, Department of Physics & Astronomy, Schuster Building. The student will be exposed to device fabrication technology for making variety of 2D-atomic crystals and nanoimprinting. Some aspect of the work might also involve electrical measurements and membrane preparation.


Eligibility
Applicants should have, or expect to achieve, at least a 2.1 honours degree or a master's (or international equivalent) in a relevant science or engineering related discipline.

Comments/amends: A minimum of a 2i class UK Masters honours degree or international equivalent in Physics/Chemistry/materials is required or a first degree with an additional Master's degree or international equivalent. Atleast one English language test is a must.

Funding
At Manchester we offer a range of scholarships, studentships and awards at university, faculty and department level, to support both UK and overseas postgraduate researchers applying for competition and self-funded projects.

For more information, visit our funding page or search our funding database for specific scholarships, studentships and awards you may be eligible for.

Comments/amends: At Manchester we offer a range of scholarships, studentships and awards at university, faculty and department level, to support both UK and overseas postgraduate researchers applying for competition and self-funded projects.

For more information, visit our funding page or search our funding database for specific scholarships, studentships and awards you may be eligible for.

Before you apply
We strongly recommend that you contact the supervisor(s) for this project before you apply. Please include details of your current level of study, academic background and any relevant experience and include a paragraph about your motivation to study this PhD project.


When applying, you'll need to specify the full name of this project, the name of your supervisor, if you already having funding or if you wish to be considered for available funding through the university, details of your previous study, and names and contact details of two referees.

Your application will not be processed without all of the required documents submitted at the time of application, and we cannot accept responsibility for late or missed deadlines. Incomplete applications will not be considered.

After you have applied you will be asked to upload the following supporting documents:

Final Transcript and certificates of all awarded university level qualifications
Interim Transcript of any university level qualifications in progress
CV
Supporting statement: A one or two page statement outlining your motivation to pursue postgraduate research and why you want to undertake postgraduate research at Manchester, any rele

Theme: Condensed Matter Physics | Supervisor: Ivan Veramarun

Our basic research on 2D nanoelectronics paves the way towards alternative computing technologies beyond the use of charge in conventional electronics. In 1965 Gordon Moore made the observation that the number of components in an integrated circuit doubles every year. Fast forward to the present day and conventional electronics is expected to reach the atomic-scale limit by the next decade. To go beyond this limitation, we explore spin currents, heat transport, and other degrees of freedom to enable alternative logic and memory devices.

We use nanotechnology as an interface between the fields of magnetism, electronics, and thermal transport. Our work integrates spintronics (Nobel Prize in Physics 2007), nanoscale thermoelectrics, and graphene, the first two-dimensional material discovered in Manchester, to develop enhanced functionality, re-programmable and 'green' electronics.

Projects:
1. Spin transport in high-quality ballistic graphene transistors.
2. Nanoscale thermoelectrics in van der Waals heterostructures.
3. Spin-hall effect and related spin-orbit phenomena in 2D materials.

Theme: Condensed Matter Physics | Supervisor: Alexander Grigorenko

Recently, plasmons and polaritons in two-dimensional (2D) systems attracted a lot of attention due to isolation and availability of various 2D materials. Among these 2D materials one can easily find dielectrics (e.g., boron-nitride), semimetals (e.g., graphene) and semiconductors (various transitional metal dichalcogenides). At the same time, ultra-thin layers of metals down to single monolayer did not receive widespread attention despite they present an interesting and important part of LEGO-like van der Waals heterostructures. Recently, it was found that ultrathin layers of metals do possess nontrivial 2D plasmons, can show high temperature superconducting transition as well as truly 2D superconducting behaviour. The study of fascinating properties of ultrathin metals and their nanostructures is a timely and exciting topic in development of flatland optics and electronics.
In our group, we have all means necessary to fabricate, characterize and optimize thin layers of metals. Various fabrication technique will be used (deposition, cleaving, electrochemistry) with the objective to achieve extremely flat and homogenous films. Optical and electrical properties will be studied using the existing equipment (spectroscopic ellipsometry, reflection and transmission spectroscopy, dc conductivity and Hall effect in large temperature and spectral ranges). New optical and electrical properties will be targeted - with emphasis on photo catalysis for green energy and high temperature superconductivity.

Theme: Condensed Matter Physics | Supervisor: Radha Boya

Our current research relates to sub-nanoscale aka angstrom-scale channels made from atomically thin 2D-materials assembled in 2D-heterostructures. The channels are akin to 3-layer sandwich (top/spacer/bottom layers, refer to the figure inset) of 2D-materials such as graphene, with cavities running through the middle of a stack. To put it simply, we make atomic-scale channels with atomically smooth walls! Using these precise channels held firmly on silicon chips, we study effects of confinement on water, ion, and gas flows which can impact the fields of molecular separation and membrane-based water desalination. We also have work ongoing on the translocation of biomolecules like DNA, proteins in such channels. Recently, we found the emergence of ionic memory and synapse-like dynamics from simple salt solutions as electrolytes confined in 2D-channels.

We have setup a new instrument on thermal scanning probe lithography in National Graphene institute, which can do precisely pattern sub-50 nm features using simply heat, and we will be recruiting a new PhD student to work with this technique.

Projects: Project 1: Ionic memory in confined nanochannels
Project 2: Thermal scanning probe lithography as a tool for fabrication of 2D material devices Project 2: Biomolecular sequencing using nanochannels.
Project 3: Confined material growth for new types of 2D materials

Theme: Condensed Matter Physics | Supervisor: Irina V Grigorieva

Prof Grigorieva's current research focuses on two main areas: (i) physics of alkali ion intercalation into 2D crystals and using intercalation as a tool to tuning tune electronic properties of layered crystals and heterostructures; (ii) unconventional superconductivity in materials with strong spin-orbit coupling.

Ion intercalation of layered van der Waals crystals underpins important applications, such as rechargeable Li ion batteries, and also provides a powerful tool to tune the material's chemical, electronic and optical properties. Yet, our understanding of the fundamentals of the intercalation process is poor: What controls the intercalation process? What determines the maximum possible concentration of the intercalating ions? How do the electronic properties of the host crystal (for example, few-layer graphene) influence the process of intercalation? In our projects we are trying to answer these fundamental questions.

In projects on superconductivity our aim is to understand how superconducting pairing works in materials with strong spin-orbit coupling. This is a little explored group of superconductors, where we recently observed signatures of unconventional (non-BCS) superconducting pairing. To this end we are using tunnelling spectroscopy and creating Josephson junctions that allow probing the symmetry of the superconducting order parameter.

Projects:
1. Understanding intercalation of 2D crystals: a physicist's approach.
2. Unconventional superconductivity in materials with strong spin-orbit coupling.

Theme: Condensed Matter Physics | Supervisor: Marcelo Lozadahidalgo

2D crystal membranes exhibit exotic phenomena. They are impermeable to all atoms and molecules but they are highly permeable to protons. They also display subatomic selectivity: deuterons, nuclei of hydrogen's isotope deuterium, permeate ~10 times slower than protons. Unexpectedly, graphene membranes are also highly sensitive to solar light: A single photon impinging on graphene induces the transport of ~10,000 protons via a novel physical effect, the photo-proton effect. Encouragingly, these properties have been found using only a couple of 2D crystals - hundreds more remained unexplored. My research is focused both on finding more exotic properties and exploiting them in a number of energy applications such as fuel cells, photocatalytic water splitting or nuclear energy. PhD projects usually involve both fundamental science and industry applications.

Theme: Condensed Matter Physics | Supervisor: Andre K Geim

Prof Geim's current research focuses on developing van der Waals (vdW) heterostructures and smart Lego-style materials based on 2D crystals. This is a very broad field of research, encompassing many new systems that allow to access electronic, optical, transport and other properties not readily found in 'natural' materials. A number of current projects focus on exploiting non-trivial topology of graphene-based heterostructures, developing new systems that allow new types of measurements (for example, a recently developed technology for fabricating designer nanochannels with monolayer precision), and studying little explored properties of graphene, boron nitride and other atomically thin crystals for transport f subatomic particles (protons, deuterons). Available PhD projects are constantly evolving and interested students are encouraged to contact Prof Geim for latest opportunities.

Theme: Condensed Matter Physics | Supervisor: Artem Mishchenko

Reactions between solids are fundamental in areas as diverse as catalysis, information storage, pharmaceuticals, electronics manufacturing, advanced ceramics, to name just a few. Controlling the spatial extent of solid-state reactions at the nanoscale will enable development of materials, programmed on an atomic level, which will facilitate many emerging applications like bioinspired smart batteries and artificial synapses for future neuromorphic electronics. Our programmable matter research is centred on van der Waals materials - layer-by-layer assembled stacks of individual atomic planes, and aim to obtain a class of new materials through interplanar chemical reactions between highly-crystalline solids in precisely controllable conditions. We focus on the two main research directions: (i) discovery and programmable synthesis of novel van der Waals materials, and (ii) study their electronic and photonic properties for various applications. By combing machine learning with automated materials synthesis, we are working on a novel approach towards materials discovery to enable future cutting-edge quantum, electronic, and photonic technologies. More details are available on https://www.2Dmatters.com 

Projects:
1. Development of autonomous materials discovery platform
2. Polariton chemistry in quantum van der Waals materials
3. Designer topology from 2.5-dimensional physics of graphene multilayers

Theme: Condensed Matter Physics | Supervisor: Andrei Golov, Paul Walmsley

Currently, the Low Temperature Group (Prof. Andrei Golov, Dr. Paul Walmsley, Dr. Ivan Skachko) investigates turbulence in superfluid 4He in the limit of zero temperatures. For further details, see:

Theme: Condensed Matter Physics | Supervisor: Laura Fumagalli

Our group focuses on the study of the physical properties of matter at the nanoscale, mainly electrical and dielectric properties, by using scanning probe microscopy techniques. In recent years we have developed scanning dielectric microscopy which is able to probe electric polarizability on the nanoscale. This is a fundamental physical property with important implications in many disciplines, from physics to chemistry and biology, and yet it remains essentially unknown on such a small scale for lack of tools with sufficiently sensitivity. Hence, the applications of scanning dielectric microscopy are countless. Currently we are particularly interested in combining it with 2D materials and state-of-the-art 2D fabrication techniques to investigate the dielectric properties of fluids and solids under extreme confinement. We recently showed the power of this approach by succeeding in the long-standing challenge of probing the polarizability of few water layers confined into nanochannels made of 2D materials. Available projects aim to continue this research to better understand the role of electric polarizability in phenomena such as surface hydration, ion solvation, molecular transport, macromolecular assembly and chemical reactions.

Projects:
1. Dielectric polarization properties of 2D confined water.
2. Dielectric polarization properties of 2D confined macromolecules.
3. Development of high-resolution dielectric microscopy.

Theme: Condensed Matter Physics | Supervisor: Roman

My research area is experimental condensed matter physics, with an emphasis on fabrication of nanoscale low-dimensional devices. The availability of novel nanoscale materials, such as nanowires and atomically thin 2-dimensional crystals is enabling the assembly and study of composite electronics and mechanical devices, as well as the exploration of fundamental physics in these low-dimensional systems. The use of modern state-of-the-art semiconductor device fabrication techniques and the development of new methods of material synthesis/manipulation are essential parts of this research, which gives an ample space to explore the new physical phenomena and can bring an impact to future technologies.

Significant part of our work is dedicated to van der Waals heterostructures assembled from 2D materials layer-by-atomic-layer, which offer unprecedented opportunities for solid state research. An important degree of freedom in 2DMH is the relative crystal rotation or twist between different atomic layers. Together with the lattice mismatch of the adjacent 2D crystals, the twist gives rise to the moiré superlattice (mSL): a long-range periodic variation of the local atomic positions with the length scale controlled by the twist angle. Before 2019 experimental twistronic investigations were largely confined to graphene/hBN, but recently other materials have gained a lot of attention.

Projects offered to PhD students continuously evolve due to fast pace of the field, at the moment:

1. Ultra-clean van der Waals heterostructures fabricated in high vacuum. To access the fascinating physics of these air sensitive 2D crystals, our team has recently built the first
in the world "UHV 2D Press" that allows the heterostructure assembly and characterisation in ultra-high vacuum. In this project you will develop UHV technology and acquire a broad range of semiconductor nanofabrication skills including robotics, UHV equipment, as well as electron and scanning probe microscopies.

2. Dynamic twist in 2D materials. This project sets to explore twisted bilayers of 2D materials that exhibit correlated electronic states. The core idea here is to employ moiré superlattice to control magnetism or superconductivity with nanometre resolution, creating periodic textures of these ground states. This project has emphasis on cutting-edge solid-state physics, nano-mechanics, robotics, optical and electronic measurements.

Theme: Condensed Matter Physics | Supervisor: Qian Yang

Theme: Physics of Fluids, Soft Matter and Liquid Crystals | Supervisor: Anne Juel, Draga Pihler-Puzovic

Research in Physics of Fluids and Soft Matter is focused on the dynamics and instabilities of complex systems, from bubble flows to soft tissues, and encompasses both curiosity-driven and industrially-relevant phenomena. Our group currently consists of 12 members including three permanent members of academic staff (Dr Draga Pihler-Puzović, Dr Finn Box and Prof Anne Juel) and a laboratory technician (Martin Quinn). Laboratory-based research into nonlinear phenomena often reveals unexpected findings, which in turn requires interpretation via mathematical modelling.

Theme: Physics of Fluids, Soft Matter and Liquid Crystals | Supervisor: Ingo Dierking

Our group primarily performs experimental research in different areas of soft condensed matter, liquid crystals, polymer modified liquid crystal composites, nanoparticle dispersions in anisotropic fluids and liquid crystal phases formed by colloidal materials, especially graphene oxide. Investigations range from fundamental physical questions to studies which are of relevance to the applications.

We use a range of in house experimental optic, electric and electro-optic techniques. For some specialized techniques and material synthesis, we collaborate with different groups world- wide.

Possible projects:
• Defect annihilation in lyotropic chromonic liquid crystals via machine learning.
• Pattern formation in hydrogen-bonded liquid crystals.
• Cellulose nanocrystal and nanofibre liquid crystals.
• Lyotropic liquid crystals from 2D materials.
• Solitons in liquid crystals.
• Functional nanoparticle dispersed liquid crystals.

Theme: Quantum Theory of Light and Matter | Supervisor: M Saeed Bahramy

Dr Mohammad Saeed Bahramy's research is focused on the study of exotic states of quantum matter using a range of computational techniques based on density functional theory, dynamical mean field theory, tight-binding modelling and, lately, machine learning. He is particularly interested in studying topological phases of matter, quantum confinement phenomena at the interface of heterogeneous materials, thermopower generation and manipulation in low-dimensional systems, strongly correlated electron systems, and superconductivity. He also seeks to understand how rich collective properties of materials, such as symmetry breaking, structural phase transition, and many-body effects, can lead to new phases of quantum matter. The ultimate goal of Dr Bahramy's research is to develop new guiding principles for the study and design of next-generation quantum materials with advanced functionalities suitable for future energy and information technologies.

Bahramy lab's current projects include:
• Development of machine-learning-based methods for designing artificial two-dimensional materials and superstructures.
• Theoretical study and design of functional materials with non-trivial topological properties.
• First-principles modelling of exotic superconductivity and magnetism in strongly correlated materials.
• Quantum simulation of quasiparticle interferences in structurally-frustrated electronic systems.
• Thermopower generation and waste heat harvesting in low-dimensional materials.

These projects will be performed in close collaboration with experimental groups in Japan (Univ. Tokyo, Univ. Osaka and RIKEN), the UK (Univ. St. Andrews, Diamond and UoM), China (Nanjing Univ.) and the USA (Stanford and Delaware Univ.).

Theme: Quantum Theory of Light and Matter | Supervisor: Michael J Godfrey

Glasses are poorly understood amorphous materials that share features of both solids and liquids: at low temperatures, a glass becomes rigid like a solid, while its microscopic structure remains virtually identical to that of a liquid. Yet how can a material with a liquid-like structure be rigid? It is a fundamental unsolved problem in physics, which also has practical importance for many technologies, the food and pharmaceutical industries, and even for the understanding of the structure of proteins and the development of organs within embryos.

Potential areas of research for a student include:

• Investigation of the connections between local microscopic structure and dynamics in glasses.
• Development and application of linear algebra techniques for computing the properties of disordered materials in low dimensions.
• Study of the so-called "Gardner transition", which has been predicted to exist deep inside the glass phase, and at which glasses might lose their brittleness and become malleable, like metals.

Theme: Quantum Theory of Light and Matter | Supervisor: Harry Miller

Dr. Harry Miller explores ways to optimise the thermodynamic behaviour of quantum systems driven far from equilibrium, with an aim to uncover universal design principles for energy-efficient quantum thermal machines and devices. This is addressed from a foundational perspective by merging ideas from stochastic thermodynamics, differential geometry and information theory.

Potential projects include:

• Developing novel theoretical methods for reducing dissipation and irreversibility in small-scale thermal processes.
• Practical applications to improve designs of quantum thermal machines such as heat engines, batteries and refrigerators.
• Optimising the energetic costs of quantum computation (eg. Information erasure, state preparation, error correction).
• Searching for quantum advantages in thermodynamic tasks (eg. Entanglement, coherence & collective effects as resources).

These projects will provide students with the opportunity to explore a wide range of topics from quantum thermodynamics, information-geometry, statistical mechanics and optimal control theory, as well a chance for collaborations with international groups from Barcelona, Pavia and Ireland.

Theme: Quantum Theory of Light and Matter | Supervisor: Alessandro Principi

I study the impact of many-body interactions on equilibrium and non-equilibrium properties of quantum materials. For example, the impact of viscous electron flow on charge, spin, orbital and thermal transport in 2D materials; the interplay between electronic and magnetic degrees of freedom; topological quantum order (e.g., quantum spin liquids) or superconductivity. I am also interested in studying applications of many-body systems and topological matter to quantum technologies (e.g., topological quantum computation), as well as their behaviour when coupled to quantized electromagnetic radiation (together with Dr. Ahsan Nazir).

The approach to these problems is mainly analytical. Numerical techniques are used to confirm/guide analytical results, numerically evaluate integrals, perform linear algebra manipulations, etc. The analytical techniques used are those of quantum field theory (Feynman diagrams, path integrals, non-equilibrium Green's functions, quantum kinetic equation, etc.) but applied to many-body problems in 2D systems.

Examples of my research interests include (please contact me for more details):

• Quantum magnetism and topological matter, in particular quantum spin liquids.
• Detecting and controlling emergent quasiparticles with anyonic statistics, with application to topological quantum computation.
• Twisted strongly-correlated 2D materials.
• The charge, spin, orbital, thermal, and thermoelectric transport in the hydrodynamic regime of electronic transport.
• The complex interplay between topology, Berry curvature and strong electron-electron interactions.

Students will learn and use advanced quantum field theory techniques. Co-supervision with other group members is possible, as well collaborations with theoretical and experimental groups in Manchester, Lancaster, Cambridge, ICFO&ICN2 (Barcelona), Pisa, MIT/Harvard (USA), Singapore.

Theme: Quantum Theory of Light and Matter | Supervisor: Thomas Elliott

Dr Thomas Elliott's research explores complex structure in quantum dynamics - and how this complexity can be harnessed - using tools from quantum information theory.

Even the smallest of quantum systems can give rise to seemingly complex behaviours. While this can make such systems hard to model with classical computers, it presents a valuable opportunity - to use quantum technologies to efficiently model and simulate other complex systems. Recently, Dr Elliott's research has focussed on how quantum computers can be used to simulate highly non-Markovian (i.e., memoryful) stochastic processes with a considerably smaller memory overhead than classically possible, and extending these results to the richer domain of adaptive agents - systems that modify their behaviour in response to environmental stimuli.

Potential project directions include:

• Exploring the interplay between quantum memory advantages and increased thermal efficiency, to e.g., design quantum protocols for extracting work from stochastic processes.
• Improving and extending the design of quantum-enhanced adaptive agents, and/or developing their potential areas of application.
• Using machine learning and related tools to enhance quantum memory advantages in stochastic simulation.
• Identifying and characterising the features of complex structure in quantum dynamics, and/or developing techniques for their efficient simulation.
The projects will be mostly analytical, with scope for a significant numerical/computational element. Students will develop a strong background in quantum information theory, and one or more of: open quantum systems; quantum stochastic processes; tensor networks; quantum thermodynamics; and quantum machine learning.

Theme: Quantum Theory of Light and Matter | Supervisor: Niels Walet

Professor Walet has broad interest in condensed matter physics, ranging from the study of
many-body effects in strongly correlated systems to the description of the properties of
graphene. His work is characterised by a mixture between theoretical and computational
approaches, where computation is used to understand the theory. Computationally intensive
projects are available as well.

A large variety of projects are available, largely in collaboration with other theorists in the
group. Examples of possible research projects include:

• The study of Majorana edge states in novels devices.
• The development of practical approaches for quantum information processing with such
devices.
• A description of the distortion of layered materials with approximate alignment.
• A correct description of flat bands and twisted bilayer graphene.
• The nature of topological effects in graphene heterostructures.
• Electronic structure of superconductivity in 2D materials.
• Development of many-body theory (coupled cluster and the functional renormalisation
group) for the study of strongly interacting systems.

Training in the relevant techniques, as well as in advanced computational methods, if
applicable, will be provided.

Theme: Quantum Theory of Light and Matter | Supervisor: Ahsan Nazir

Dr. Ahsan Nazir offers theoretical projects on the thermodynamics and non-equilibrium
dynamics of open quantum systems. Open quantum systems theory describes the
behaviour of quantum systems that are not isolated, but instead in contact with their surrounding environmental degrees of freedom. It is a topic of primary importance in physics and chemistry, and is becoming increasingly relevant in biology as well. Dr. Nazir develops new theoretical techniques to understand the behaviour of open quantum systems both in and out of equilibrium. Applications range from quantum thermodynamics to solid-state quantum technology, quantum transport, and the behaviour of molecular nanosystems.

Potential projects include:

• Fundamental developments in the theory of open quantum systems and applications to
many-body systems;
• the impact of quantum correlations on the laws of thermodynamics and quantum scale
thermal machines;
• the effects of environmental interactions in solid-state quantum technology (with
established experimental collaborations);
• strong light-matter interactions in quantum electrodynamics;
• vibrational influences in the optical and electronic properties of natural and artificial
molecular aggregates, with applications to solar energy harvesting.

Theme: Quantum Theory of Light and Matter | Supervisor: Vladimir Falko

Professor Vladimir Fal'ko studies electronic and optical properties of two-dimensional (2D)
materials and their heterostructures. 2D materials are atomically thin crystals which electronic
and optical properties are dominated by quantum physics not only in cryogenic conditions, but
even at the room temperature. His current projects include:

• Many-body phases of electronic liquids in 2D materials, including the quantum Hall effect
in 2D materials with multi-valley spectra, where electrons are characterised by valley
quantum numbers additional to their spin state;
• quantum properties of minibands generated by moiré superlattices generic for
heterostructures of 2D materials with slightly incommensurate periods and for twisted
homo-bilayers of all 2D materials;
• modelling optical properties of 2D materials, from THz range (intersubband transitions in
few-layer films and modelling of new types of cascade lasers) to single photon emissions
from excitonic complexes (trions, biexcitons, quintons, etc) in heterostructures, including
the influence of moiré superlattice effects.

These projects will enable students to learn field theoretical methods in condensed matter theory; analytical and computational quantum transport theory; group theory and symmetry applications in solid state physics. The studies will be carried out in collaboration with experimental groups involved in the European Graphene Flagship at Manchester, Geneva, ETH Zurich, LNCMI-CNRS in Grenoble, and our partners in the European Quantum Technologies Flagship at Cambridge and ICFO in Barcelona.

Theme: Algebra, logic and number theory | Supervisor: Omar Leon sanchez

Differential rings and algebraic differential equations have been a crucial source of examples for model theory (more specifically, geometric stability theory), and have had numerous application in number theory, algebraic geometry, and combinatorics (to name a few).
In this project we propose to establish and analyse deep structural results on the model theory of (partial) differential fields. In particular, in the setup of differentially large fields.
There are interesting questions around inverse problems in differential Galois theory that can be address as part of this project. On the other hand, there are (still open) questions related to the different notions of rank in differentially closed fields; for instance: are there infinite dimensional types that are also strongly minimal? This is somewhat related to the understanding of regular types, which interestingly are quite far from being fully classified. A weak version of Zilber's dichotomy have been established for such types, but is the full dichotomy true?

Theme: Algebra, logic and number theory | Supervisor: Martin Orr

Project: Algebraic invariants of abelian varieties

Abelian varieties are higher-dimensional generalisations of elliptic curves, objects of algebraic geometry which are of great interest to number theorists. There are various open questions about how properties of abelian varieties vary across a families of abelian varieties.

The aim of this project is to study the variation of algebraic objects attached to abelian varieties, such as endomorphism algebras, Mumford-Tate groups or isogenies. These algebraic objects control much of the behaviour of the abelian variety. We aim to bound their complexity in terms of the equations defining the abelian variety.

Potential specific projects include:
(1) Constructing "relations between periods" from the Mumford-Tate group. This involves concrete calculations of polynomials, similar in style to classical invariant theory of reductive groups.
(2) Understanding the interactions between isogenies and polarisations of abelian varieties. This involves calculations with fundamental sets for arithmetic group actions, generalising reduction theory for quadratic forms.

A key tool is the theory of reductive groups and their finite-dimensional representations (roots and weights).

Theme: Algebra, logic and number theory | Supervisor: Omar Leon sanchez

Model theory is a branch of Mathematical Logic that has had several remarkable applications with other areas of mathematics, such as Combinatorics, Algebraic Geometry, Number Theory, Arithmetic Geometry, Complex and Real Analysis, Functional Analysis, and Algebra (to name a few). Some of these applications have come from the study of model-theoretic properties of fields equipped with a family of operators. For instance, this includes differential/difference fields. In this project, we look at the model theory of fields equipped with general classes of operators and also within certain natural classes of arithmetic fields (such as large fields). Several foundational questions remain open around what is called "model-companion", "elimination of imaginaries", and the "trichotomy", this is a small sample of the problems that can be tackled.

Theme: Algebra, logic and number theory | Supervisor: Richard Webb

A powerful technique for studying groups is to use their actions by isometries on metric spaces. Properties of the action can be translated into algebraic properties of the group, and vice versa. This is called geometric group theory, and has played a key role in different fields of mathematics e.g. random groups, mapping class groups of surfaces, fundamental groups of 3-manifolds, the Cremona group.

In this project we will study the homeomorphisms of a surface by using geometric group theoretic techniques recently introduced by Bowden, Hensel, and myself. This is a new research initiative at the frontier between dynamics, topology, and geometric group theory, and there are many questions waiting to be explored using these tools. These range from new questions on the relationship between the topology/dynamics of homeomorphisms and their action on metric spaces, to older questions regarding the algebraic structure of the homeomorphism group.

Theme: Algebra, logic and number theory | Supervisor: Philip Dittmann

A valuation on a field is a standard notion of a function abstractly measuring the size of field elements. This is one of the standard ways of obtaining field topologies, and is at least partially motivated by algebraic number theory and algebraic geometry, although the theory can be developed without those applications in mind.
Valued fields form a rich subject of study for model theory. Notable success stories here are in particular quantifier elimination results for the field of p-adic numbers and for power series fields in characteristic zero. The theory in positive characteristic is much less well understood, although some restricted progress has been made in recent years. In this project, we will bring together some of these new methods to analyse previously unexplored theories of valued fields.

Theme: Algebra, logic and number theory | Supervisor: Vahagn Aslanyan

The Existential Closedness problem asks when systems of equations involving field operations and certain classical functions of a complex variable, such as exponential and modular functions, have solutions in the complex numbers. There are conjectures predicting when such systems should have solutions. The general philosophy is that when a system is not "overdetermined" (e.g. more equations than variables) then it should have a solution. The notion of an overdetermined system of equations is related to Schanuel's conjecture and its analogues and is captured by some purely algebraic conditions.

The aim of this project is to make progress towards the Existential Closedness conjectures (EC for short) for exponential and automorphic functions (and the derivatives of automorphic functions). These include the usual complex exponential function, as well as the exponential functions of semi-abelian varieties, and modular functions such as the j-invariant. Significant progress has been made towards EC in recent years, but the full conjectures are open. There are many special cases which are within reach and could be tackled as part of a PhD project. Methods used to approach EC come from complex analysis and geometry, differential algebra, model theory (including o-minimality), tropical geometry.

Potential specific projects are: (1) proving EC in low dimensions (e.g. for 2 or 3 variables), (2) proving EC for certain relations defined in terms of the function under consideration, e.g. establishing new EC results for "blurred" exponential and/or modular functions, (3) proving EC under additional geometric assumptions on the system of equations, (4) using EC to study the model-theoretic properties of exponential and automorphic functions.

Theme: Analysis, geometry and dynamical systems | Supervisor: Lasse Rempe

In one-dimensional holomorphic dynamics, we consider a function f of a complex variable as a dynamical system whose state is described by a complex number. If z is the state of the system today, then f(z) describes its next state, f(f(z)) the following one, and so on. Even simple functions can lead to highly non-trivial phenomena, and the field has connections to many modern fields of mathematics, including hyperbolic geometry, fractal geometry, ergodic theory, number theory, topology, and many others. Work in the field tends to be highly geometric, and often gives rise to beautiful images such as the famous "Mandelbrot set".

My work is particularly concerns with the case when the function f is "transcendental entire", that is, a holomorphic self-map of the complex plane that is not a polynomial in z. Examples are exponential or trigonometric functions, but the class of transcendental entire functions is much wider than these examples suggest. Transcendental dynamics is a field that was founded a century ago by Fatou, but has seen considerable progress in recent years, with a number of long-standing open questions being solved. Below are two possible projects among many.

1. In a recent paper by Martí-Pete, Waterman and myself (accepted for publication in Journal of the American Mathematical Society as of 2025), we show that any compact subset of the plane with connected complement can be realised as a natural (wandering) subset of the dynamical plane of some transcendental entire function, and use this to solve a number of open problems. It is also observed that the techniques can also be applied to certain unbounded sets; we use this to construct a counterexample to a famous conjecture of Eremenko. This project would consider the realisation of unbounded wandering sets for transcendental entire functions more systematically, building on the aforementioned work.

2. In a paper from 2009 (published in Acta Mathematica), I show a certain "rigidity" phenomenon for a class of transcendental entire functions, which as had important consequences for the study of these functions. Similar phenomena should hold for classes of meromorphic functions (which are allowed to have poles). The goal of this project would be to establish such a generalisation.

There are many other exciting directions to pursue, and a project can be chosen depending on the prospective students' interests and existing knowledge. Anyone interested in pursuing doctoral studies in holomorphic dynamics or adjacent areas should, in the first instance, contact me to arrange an informal chat.

Theme: Mathematics in the life sciences | Supervisor: Thomas House

Understanding patterns of disease at the population level - Epidemiology - is inherently a quantitative problem, and increasingly involves sophisticated research-level mathematics and statistics in both infectious and chronic diseases. The details of which diseases and mathematics offer the best PhD directions are likely to vary over time, but this broad area is available for PhD research.

Theme: Probability, financial mathematics and actuarial science | Supervisor: Robert Gaunt

Stein's method is a powerful (and elegant) technique for deriving bounds on the distance between two probability distributions with respect to a probability metric. Such bounds are of interest, for example, in statistical inference when samples sizes are small; indeed, obtaining bounds on the rate of convergence of the central limit theorem was one of the most important problems in probability theory in the first half of the 20th century.

The method is based on differential or difference equations that in a sense characterise the limit distribution and coupling techniques that allow one to derive approximations whilst retaining the probabilistic intuition. There is an active area of research concerning the development of Stein's method as a probabilistic tool and its application in areas as diverse as random graph theory, statistical mechanics and queuing theory.

There is an excellent survey of Stein's method (see below) and, given a strong background in probability, the basic method can be learnt quite quickly, so it would be possible for the interested student to make progress on new problems relatively shortly into their PhD. Possible directions for research (although not limited) include: extend Stein's method to new limit distributions; generalisations of the central limit theorem; investigate `faster than would be expected' convergence rates and establish necessary and sufficient conditions under which they occur; applications of Stein's method to problems from, for example, statistical inference.

Literature: Ross, N. Fundamentals of Stein's method. Probability Surveys 8 (2011), pp. 210-293.

Theme: Probability, financial mathematics and actuarial science | Supervisor: Malwina Luczak

Several projects are available, studying idealised Markovian models of epidemic, population and network processes. The emphasis will mostly be on theoretical aspects of the models, involving advanced probability theory. For instance, there are a number of stochastic models of epidemics where the course of the epidemic is known to follow the solution of a differential equation over short time intervals, but where little or nothing has been proved about the long-term behaviour of the stochastic process. Techniques have been developed for studying such problems, and a project might involve adapting these methods to new settings. Depending on the preference of the candidate, a project might involve a substantial computational component, gaining insights into the behaviour of a model, via simulations, ahead of proving rigorous theoretical results.

Theme: Probability, financial mathematics and actuarial science | Supervisor: Jose Pedraza ramirez

The proposed research focuses on Lévy processes, optimal stopping problems, and optimal prediction problems. Lévy processes are widely used models in finance and risk theory, offering a flexible framework for capturing the complex stochastic behaviour found in financial markets and insurance. They allow for both continuous changes and discrete jumps, accommodating the often unpredictable and abrupt shifts seen in real-world phenomena. Unlike models based solely on Brownian motion, Lévy processes can describe sudden, large fluctuations, making them particularly useful for accurately modelling financial and insurance dynamics.

Optimal stopping problems involve determining the optimal timing for specific actions to maximise expected payoffs or minimise costs based on the evolution of a stochastic process. In finance and insurance, many applications are rooted in optimal stopping theory, including option pricing and the valuation of variable annuities. For example, optimal stopping is crucial for policy termination or renewal, claim settlement, and portfolio adjustments in insurance. By applying this theory, insurers can make strategic timing decisions to enhance profitability, reduce risk, or achieve particular financial objectives.

On the other hand, optimal prediction problems focus on forecasting the timing of events that depend on future information, such as last passage times, by using stopping times. In the literature, these problems have been applied to predict relevant quantities, such as maximum or minimum asset prices or critical moments like a company's time to ruin in a finite or infinite time horizon.

These kinds of projects are theoretical/mathematical, so a solid foundation in probability and measure theory, Brownian motion, martingales, stochastic calculus, and Markov processes is essential for this project.

Theme: Statistics, inverse problems, uncertainty quantification and data science | Supervisor: Nilabja Guha

In many applications such as biological sciences, social science, and engineering, we encounter high-dimensional observations. Bayesian approach can provide a flexible modeling framework for underlying structures in high dimension such as underlying covariance structure, conditional dependency graphs etc. With the change in data-generating mechanism, these high-dimensional structures may change with time, where the change can depend on latent factors or variables.


These projects will focus on developing a comprehensive Bayesian learning framework for this broad class of problems while focusing on specific applications. The goal would be to develop computationally efficient and scalable Bayesian learning methodologies with practical applications and establish relevant theoretical properties.

Theme: Statistics, inverse problems, uncertainty quantification and data science | Supervisor: Nilabja Guha

In many applications, such as biological sciences, social science, and engineering we encounter high-dimensional observations. Bayesian approach can provide a flexible modeling framework for underlying structures in high dimension such as underlying covariance structure, conditional dependency graphs etc. With the change in data-generating mechanism, these high-dimensional structures may change with time, where the change can depend on latent factors or variables.


These projects will focus on developing a comprehensive Bayesian learning framework for this broad class of problems while focusing on specific applications. The goal would be to develop computationally efficient and scalable Bayesian learning methodologies with practical applications and establish relevant theoretical properties.

Theme: Statistics, inverse problems, uncertainty quantification and data science | Supervisor: Yang Han

Dr Yang Han, Senior Lecturer (Associate Professor) in Statistics at The University of Manchester, is recruiting PhD students to start in September 2026. Her research interests include Simultaneous Inference, Multiple Testing, Statistical Machine Learning, and Personalised Medicine. To apply, please send your CV to: yang.han@manchester.ac.uk . In numerous applications, simultaneous inferences must be made, such as testing multiple hypotheses or determining plausible ranges for several parameters. Ensuring that these inferences are simultaneously correct with a high level of confidence is critical in fields including finance, industry, and the medical and health sciences. Specific PhD projects can be tailored within the areas of simultaneous inference and multiple testing.

Theme: Statistics, inverse problems, uncertainty quantification and data science | Supervisor: Ines Henriques-Cadby, Olatunji Johnson

A range of projects are available on the topic of statistical spatial and temporal modelling for crime.

These projects will focus on developing novel methods for modelling crime related events in space and time, and applying these to real world datasets, mostly within the UK, but with the possibility to use international datasets. Some examples of recent applications include spatio-temporal modelling of drug overdoses and related crime.

These projects will aim to use statistical spatio-temporalpoint processes methods, Bayesian methods, and machine learning methods.

The project will require the candidate to be proficient in a modern programming language (e.g., R or Python).

Applicants should have achieved a first-class degree in Statistics or Mathematics, with a significant component of Statistics, and be proficient in a statistical programming language (e.g., R, Python, Stata, S).

We strongly recommend that you contact the supervisor(s) for this project before you apply. Please send your CV and a brief cover letter to ines.henriques-cadby@manchester.ac.uk before you apply.

At Manchester we offer a range of scholarships, studentships and awards at university, faculty and department level, to support both UK and overseas postgraduate researchers.

For more information, visit our funding page or search our funding database for specific scholarships, studentships and awards you may be eligible for.