LMS Joint Research Group Inverse Problems: Theory and Applications

An example of artefacts which occur in reconstruction from the geodesic ray transform in the presence of conjugate points.

In inverse problems we try to recover an unknown $$x$$ from some given data $$d$$. A very general mathematical model for this situation is $$d = F(x) + \epsilon$$ where we have a known "forward map" $$F$$ giving a model of how the data are related to the parameters to be determined, and some random noise $$\epsilon$$ representing errors in measurement. In many cases, the forward map F itself involves solving a differential equation, or some other type of problem. Researchers working on inverse problems may attempt to devise algorithms to find $$x$$ given $$d$$, or may study properties of this equation for specific instances of $$F$$.

Applications of inverse problems are numerous and appear in physics, engineering, biology, and medicine, but also many other areas. One attractive aspect of inverse problems for mathematicians is that research in the field spans the gamut from pure to applied, and readily allows for collaboration between researchers working on theoretical questions with those working on computational or applied problems.

The main function of this group is to plan workshops and short, one-day, courses across the United Kingdom on inverse problems. With these workshops we hope to:

• Build a strong research network in inverse problems within the UK, and foster connections with research groups abroad.
• Help to connect isolated researchers in the field who may be the only ones at their university working in inverse problems.
• Provide opportunities for young researchers including PhD students and post-docs to learn from experts outside their own universities, and begin to build a network of contacts.
• Promote the UK as an international centre for cutting edge research on inverse problems.

Each meeting will be jointly funded by the London Mathematical Society (LMS), and the local institution.