# Student projects

For opportunities at the

I am always interested in working with students (B.Sc./M.Sc.) on projects in the direction of probability theory (as broadly defined). I am especially interested in projects in which there is an interplay between probability theory and other areas of mathematics, for example analysis (PDEs, calculuas of variations, dynamical systems), optimisation, machine learning/data science; the focus can be skewed to fit the interests of the student.

If you think you are interested in working on a thesis project with me, feel free to send an email and we can discuss further. In particular, for students thinking about possibly doing a PhD in probability theory (broadly construed) there is the possibility to work on research-related topics for the thesis.

Below are some examples of potential thesis topics, you can also see my teaching section for an overview of past projects.

Statistical mystery of the prime numbers (B.Sc.)

P-hacking and reproducibility: The on-going crisis in statistics (B.Sc.)

Non-convex learning via stochastic gradient methods using infinite swapping (M.Sc.)

Metastability in statistical learning (M.Sc.)

Deep learning for solving PDEs: theory and algorithms (M.Sc.)

Corrections for anisotropic bootstrap percolation using calculus of variations and Monte Carlo (M.Sc.)

Sample size in importance sampling: Interpreting Chatterjee and Diaconis' bound using large deviations (M.Sc.)

Efficient sampling dynamics for mean-field models in statistical physics (M.Sc.)

Neural tangent models vs. neural networks: beyond quadratic functions (M.Sc.)

Monte Carlo methods for variance reduction based on neural networks (M.Sc.)

**Ph.D. or postdoc level**see Open positions.I am always interested in working with students (B.Sc./M.Sc.) on projects in the direction of probability theory (as broadly defined). I am especially interested in projects in which there is an interplay between probability theory and other areas of mathematics, for example analysis (PDEs, calculuas of variations, dynamical systems), optimisation, machine learning/data science; the focus can be skewed to fit the interests of the student.

If you think you are interested in working on a thesis project with me, feel free to send an email and we can discuss further. In particular, for students thinking about possibly doing a PhD in probability theory (broadly construed) there is the possibility to work on research-related topics for the thesis.

Below are some examples of potential thesis topics, you can also see my teaching section for an overview of past projects.

Statistical mystery of the prime numbers (B.Sc.)

P-hacking and reproducibility: The on-going crisis in statistics (B.Sc.)

Non-convex learning via stochastic gradient methods using infinite swapping (M.Sc.)

Metastability in statistical learning (M.Sc.)

Deep learning for solving PDEs: theory and algorithms (M.Sc.)

Corrections for anisotropic bootstrap percolation using calculus of variations and Monte Carlo (M.Sc.)

Sample size in importance sampling: Interpreting Chatterjee and Diaconis' bound using large deviations (M.Sc.)

Efficient sampling dynamics for mean-field models in statistical physics (M.Sc.)

Neural tangent models vs. neural networks: beyond quadratic functions (M.Sc.)

Monte Carlo methods for variance reduction based on neural networks (M.Sc.)