CURRICULUM VITAE for Nikita Sidorov

A. Personal Record

Born: 1968

Nationality: British, Russian (dual)

Address: School of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom.

Position held: Lecturer in Pure Mathematics

Fax: (0161) 275 5819 (+44-161-275 5819 from overseas)

Work phone: (0161) 200 36 87 (+44-161-2003687 from overseas)

E-mail: sidorov@manchester.ac.uk

Home page: http://www.maths.manchester.ac.uk/~nikita/

Qualifications:

Ph.D. in Mathematics (Candidate of Physical and Mathematical Sciences), Steklov Mathematical Institute at St. Petersburg, 1996.

M.Sc. in Mathematics (Summa cum Laude), St. Petersburg State University, 1992.

Memberships:

St. Petersburg Mathematical Society (since 1996)

Appointments:

  1. 11/04 – present: Lecturer in Pure Mathematics
  2. 11/01 – 11/04: Named Research Associate in the Department of Mathematics at UMIST, Manchester.
  3. 11/98 – 11/01: Research Associate in the Department of Mathematics at UMIST, Manchester
  4. 09/96 - 07/97: Postdoctoral fellow at the Institut de Mathématiques de Luminy, Marseilles, France.
  5. 09/92 - 09/96: Assistant Professor at Baltic State University of Technology, St. Petersburg, Russia.

Invited position:

6/99-7/99: Invited professor at the University Paris-7.

 

B. Research and Academic/Professional Standing

Refereed Publications:

  1. K. Hare, I. Morris, N. Sidorov and J. Theys, An explicit counterexample to the Lagarias-Wang finiteness conjecture, Advances in Mathematics 226 (2011), 4667-4701.
  2. D.-J. Feng and N. Sidorov, Growth rate for beta-expansions, Monatshefte für Mathematik 162 (2011), 41-60.
  3. N. Sidorov and B. Solomyak, On the topology of sums in powers of an algebraic number, Acta Arithmetica 149 (2011), 337-346.
  4. K. Hare and N. Sidorov, A lower bound for Garsia’s entropy for certain Bernoulli convolutions, LMS Journal of Computation and Mathematics 13 (2010), 130-143.
  5. J.-P. Allouche, M. Clarke and N. Sidorov, Periodic unique beta-expansions: the Sharkovskiĭ ordering, Ergodic Theory and Dynamical Systems 29 (2009), 1055-1074.
  6. N. Sidorov, Expansions in non-integer bases: Lower, middle and top orders, Journal of Number Theory 129 (2009), 741-754.

7.      N. Sidorov, Combinatorics of linear iterated function systems with overlaps, Nonlinearity 20 (2007) 1299-1312.

8.      E. Olivier, N. Sidorov and A. Thomas, On the Gibbs properties of Bernoulli convolutions related to β-numeration in multinacci bases, Monatshefte für Mathematik 145 (2005), 145-174.

9.      D. Broomhead and N. Sidorov, Mutual information and capacity of a linear digital channel, Nonlinearity 17 (2004), 2203-2223.

10.  D. Broomhead, J. Montaldi and N. Sidorov, Golden gaskets: variations on the Sierpiński sieve, Nonlinearity 17 (2004), 1455-1480.

  1. N. Sidorov, Universal β-expansions, Periodica Mathematica Hungarica 47 (2003), 221-231.

12.  N. Sidorov, Ergodic-theoretic properties of certain Bernoulli convolutions, Acta Mathematica Hungarica 101 (2003), 345-355.

13.  N. Sidorov, Almost every number has a continuum of β-expansions, American Mathematical Monthly 110 (2003), 838-842.

  1. N. Sidorov and B. Solomyak, Spectra of Bernoulli convolutions as multipliers in Lp on the circle, Duke Mathematical Journal 120 (2003), 353-370.
  2. N. Sidorov, Arithmetic Dynamics, London Mathematical Society Lecture Note Series 310 (2003), 145 -189.

16.  M. Nicol, N. Sidorov and D. Broomhead, On the fine structure of stationary measures in systems which contract-on-average, Journal of Theoretical Probability 15 (2002), 715-730.

17.  N. Sidorov, An arithmetic group associated with a Pisot unit, and its symbolic-dynamical representation, Acta Arithmetica 101 (2002), 199-213.

18.  N. Sidorov, Bijective and general arithmetic codings for Pisot automorphisms of the torus, Journal of Dynamical and Control Systems 7 (2001), 447-472.

19.  P. Glendinning and N. Sidorov, Unique representations of real numbers in non-integer bases, Mathematical Research Letters 8 (2001), 535-543.

20.  J. M. Dumont, N. Sidorov and A. Thomas, Number of representations related to a linear recurrent basis, Acta Arithmetica 88 (1999), 371-394.

21.  A. Vershik and N. Sidorov, Bijective codings of toral automorphisms, and binary quadratic forms (in Russian), Russian Mathematical Surveys 53 (1998), 1106-1107.

22.  N. Sidorov and A. Vershik, Bijective arithmetic codings of hyperbolic automorphisms of the 2-torus, and binary quadratic forms, Journal of Dynamical and Control Systems 4 (1998), 365-399.

23.  N. Sidorov and A. Vershik, Ergodic properties of Erdös measure, the entropy of the goldenshift, and related problems, Monatshefte für Mathematik 126 (1998), 215-261.

24.  N. Sidorov, Sum-of-digits functions for certain non-stationary bases, Zapiski Nauchn. Seminarov POMI 240 (1997), 257-267 (in Russian); English transl. Journal of Mathematical Sciences. 96 (1999), 3609-3615.

25.  N. Sidorov, Singularity and absolute continuity of measures associated with a rotation of the circle, Zapiski Nauchn. Seminarov POMI 223 (1995) 323-336 (in Russian); English transl. Journal of Mathematical Sciences 87 (1997), 4187-4198.

26.  N. Sidorov, Laws of large numbers and the central limit theorem for sequences of coefficients of rotational expansions, Zapiski Nauchn. Seminarov POMI 223 (1995), 313-322 (in Russian); English transl. Journal of Mathematical Sciences 87 (1997), 4180-4186.

27.  A. Vershik and N. Sidorov, Arithmetic expansions associated with a rotation of the circle and with continued fractions, St. Petersburg Mathematical Journal 5 (1994), 1121-1136.

To appear:

28.  I. D. Morris and N. Sidorov,   On a Devil's staircase associated to the joint spectral radii of a family of pairs of matrices, to appear in Journal of European Mathematical Society (JEMS).

  1. K. Hare, I. Morris and N. Sidorov, Extremal sequences of polynomial complexity, to appear in Mathematical Proceedings of Cambridge Philosophical Society.

Conference proceedings:

30.  N. Sidorov, Optimizing properties of balanced words, Electr. Proc. Theoret. Comp. Sci. 63 (2011), 240-246.

31.  M. Nicol, N. Sidorov and D. Broomhead, Semigroups of functions and the structure of stationary measures in systems which contract-on-average, in `Trends in Mathematics: Bifurcations, Symmetry and Patterns’, Birkhäuser Verlag Basel/Switzerland, 2003, pp 181-187.

Refereeing:

Refereed for the following journals:

·         Advances in Mathematics

·         Journal of the London Mathematical Society

·         Transactions of the American Mathematical Society

·         Mathematical Proceedings of the Cambridge Philosophical Society

·         Theoretical Computer Science

·         Ergodic Theory & Dynamical Systems

·         Discrete & Continuous Dynamical Systems

·         Mathematika

·         Journal of Statistical Physics

·         Nonlinearity

·         Acta Arithmetica

·         Journal de la Théorie de Nombres de Bordeaux

·         International Journal of Number Theory

·         Monatshefte fuer Mathematik

·         Fundamenta Mathematicae

·         St Petersburg Journal of Mathematics

I am a reviewer for the AMS Mathematical Reviews (MathSciNet).

Talks at conferences:

·         Arithmétique, Automates et Systèmes Dynamiques, Marseille, 1999.

·         Dynamical Systems and Ergodic Theory, Katsiveli, 2000.

·         Combinatorics, Dynamics, Probability, Stockholm, 2000.

·         Random Walks, Vienna, 2001.

·         Arithmetic, Automata and Asymptotics, Graz, 2002.

·         Dynamics Symposium, Warwick, 2003.

·         The Mathematics and Physics of Aperiodic Order, Greifswald, 2003.

·         Analysis and Geometry on Random Structures, Lille, 2004.

·         Bernoulli Convolutions and Beta-Expansions, Manchester, 2004.

·         CANT, Liege, 2006.

·         Dynamical Systems and Statistical Mechanics, Durham, 2006.

·         Dynamical aspects of numeration, Paris, 2006.

·         Chaotic Properties of Dynamical Systems, Warwick, 2007.

·         Dynamical Aspects of Number Systems, Rome, 2008.

·         Dynamical Numbers, Max-Planck Institute, Bonn, 2009.

·         Digital expansions, dynamics and tilings, Aussois, 2010.

·         EPSRC Symposium Workshop on Dynamical Systems and Dimension, Warwick, 2011.

·         WORDS, Prague, 2011.

·         Ergodic Theory and Dynamical Systems: Perspectives and Prospects, Warwick, 2012.

 

Graduate Students Supervised

  • Jonathan Wacks, 2005, (MSc, Degree with distinction).
  • Dintle Kagiso, 2009 (MSc, self-funded, Degree with distinction).
  • Siti Said, 2011 (MSc, self-funded, Degree with distinction).
  • Rafael Alcaraz Barrera (PhD, self-funded, 2010 - ).
  • Simon Baker (PhD, 2010-)
  • Lyndsey Clark (PhD, 2012-)

 

I also supervised a 3rd Year Project (Matthew Clarke, 2007), Mark: 99. Matthew was shortlisted for the SET Award for the mathematics student of the year.

Organization and Promotion of Research

I was the organizer of the international workshop “Bernoulli Convolutions and Beta-Expansions” in Manchester (September 8-10, 2004). This event has brought together various leading figures in the field (B. Solomyak, M. Pollicott, V. Komornik, K. Dajani, M. Rams) which has resulted in their fruitful collaboration and subsequent joint publications. 

I am an active member of MathOverflow, with a reputation over 1,000.

Statement on Research

The majority of my work is in an area related to Dynamical Systems, Number Theory and Geometric Measure Theory. Recently I got interested in questions related to growth of matrix products.

Here are some topics I am (or have been) working on:

  1. Beta-expansions and other arithmetic representations of real numbers in non-integer bases;
  2. Bernoulli convolutions and other singular measures of arithmetic nature;
  3. Joint spectral radius and the Finitemess Conjecture;
  4. Iterated function systems (IFSs) and their applications to digital channels;
  5. Fractals;
  6. Dimension theory;
  7. Pisot numbers;
  8. Arithmetic codings of ergodic transformations of algebraic origin;
  9. Sum-of-digit functions and other summatory functions.

My most significant contributions to date are as follows:

1.      In 1998 Vershik and I published a paper which remains my most quoted one. We studied in detail ergodic, arithmetic and combinatorial properties of an important singular measure on the interval – the Erdös measure.

2.      In 2003 Boris Solomyak and I published a paper in which we answered an old question of P. Sarnak (Princeton) on the closure of the set of Fourier coefficients of the Bernoulli convolution parametrized by a Pisot number. We showed that this set is infinite countable, which yields the countability of the spectrum of the corresponding convolution operator.

3.      In 2004 David Broomhead, James Montaldi and I published a paper on fractals. Its main result indicates that even if the `open set condition’ fails, there are still interesting cases for which one can compute the dimension of the attractor explicitly.

4.      In a recent paper Boris Solomyak and I have made a breakthrough in an area introduced in the 1990s by Erdös and his collaborators. More precisely, we have shown that the set of finite sums in nonnegative powers of q>1 with coefficients 0 and 1 is dense in R if q is not a Perron number.

5.      In my recent paper (joint with Kevin Hare, Ian Morris and Jacques Theys) we made a breakthrough by finding an explicit counterexample to the `Finiteness Conjecture’. This conjecture states that for any finite collection of matrices the maximal growth of their long products can be always attained by taking periodic products. Our construction involves Sturmian sequences and results from combinatorics on words and ergodic theory. Two follow-on papers will soon appear.

I have 485 citations. My H-index is 15 (Google Scholar).

C. Teaching

Current teaching duties

  1. MATH20142 Complex Analysis, a 2nd year undergraduate mathematics course for the joint honours students (2005/06 – present, 36 contact hours, 85 students)
  2. MATH 31001/41001/61001 Linear Analysis, a 3rd year undergraduate mathematics course with extra lectures and examples for the graduate students (2006/2007 – present, 36/48 contact hours, 85 students)
  3. Supervisions for MATH10101 Sets, Numbers and Functions (2005 – present, 24 contact hours, 20 students)
  4. Service teaching (Foundation Year) (2006 – present, 12 contact hours, 25 students)

 

Past teaching duties

  • 117b Topics in Pure and Experimental Mathematics (2005) – continued fractions and Diophantine approximations;
  • MT3502 Calculus of Several Variables (2005-2007);
  • MT2292 Discrete Mathematics (2006);
  • MATH40111 Modern Analysis (2006).

D. Administration

I am the organizer of the Dynamical Systems seminar since 2006. Our seminar meets approximately once a week during the semester time and sometimes in summer for an occasional visiting speaker. My job in this capacity involves contacting potential speakers, arranging their visits (in case of an external speaker) and taking care of a speaker during the seminar day.

 

I am a member of the Projects Committee.