Random Dynamics and Geometric Analysis

The project focusses on the theory of stochastic processes and their applications. We are particularly interested in the interactions between certain random dynamics and the geometry of the space on which they are defined. The focus is on three parallel ambitious research directions:

1. Stochastic partial differential equations on fractals, with an emphasis  on the stochastic heat equation and the parabolic Anderson model.
2. Diffusion methods in sub-Riemannian geometry with a focus on novel notions of curvature bounds.
3. Random matrices with a focus on its connections with the theory of flag manifolds.

The project will open 3 graduate Phd positions and 3 postdoc positions over the 5 years project.

We acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon Europe research and innovation programme (RanGe project, Grant Agreement No. 101199772).

The project run from 1 January 2026 until 1 January 2031.