#### Eric Hester

- Asymptotic analysis of PDEs
- Spectral algorithms for numerical PDE solvers
- Multiphase fluid mechanics

Department of Mathematical Sciences

**Dr Yury Korolev**

Research interests:

- Inverse problems and imaging
- Machine learning in infinite dimensions
- Non-smooth variational problems

Yury uses functional analysis to better understand numerical algorithms used in machine learning, inverse problems, and mathematical imaging. He studies neural networks as functions in certain function spaces where they achieve efficient approximation rates (that is, rates that do not depend on the dimension of the input space). He also develops data-driven regularisation methods for ill-posed inverse problems and applies them in imaging (primarily, light microscopy) in collaboration with other departments. Yury is also interested in nonlinear eigenvalue problems (that is, eigenvalue problems for non-linear and even set-valued operators such as the subdifferential of a convex function) and their applications in data science.

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