I'm happy to supervise student projects in a variety of topics:

• Large deviations for stochastic processes
• Random (geometric) graphs
• Stochastic processes in manifolds
• Random walks
• Connections between analysis and probability theory
• Probability theory in general

Feel free to contact me to discuss interests and possibilities for a project.

I have the following more specified project(s):

1. Concentration inequalities in Riemannian manifolds

Concentration inequalities are concerned with showing how the mass of a probability distribution concentrates around a typical value, usually its expectation. For random walks with bounded increments, this is known as Hoeffding's inequality. The notion of a random walk may also be extended to a Riemannian manifold. Such a random walk is constructed recursively by following pieces of geodesics, therefore called a geodesic random walk. The aim of this project is to extend Hoeffding's result to such geodesic random walks.

An important extension of Hoeffding's result is Azuma-Hoeffding's inequality, which gives a similar result for martingales with bounded differences. A martingale is a stochastic process which resembles a 'fair game'. Martingales can also be defined in manifolds with a connection. Therefore, a natural follow-up question to the above is whether Azuma-Hoeffding's inequality may be extended to hold also for manifold-valued martingales.