"The project RanGe is at the interface of Probability theory, Analysis and Geometry. The primary objective is to investigate the interactions between certain random dynamics and the geometry of the space in which they occur. This interaction is fruitful in both directions: In some parts of the proposed research, we will prove new properties of stochastic processes based on the known geometric characteristics of the environment; in other parts, we will use stochastic processes and techniques originating from probability theory to prove new geometric results. The focus will be on three parallel ambitious research directions:

• The theory of stochastic partial differential equations on fractal spaces.
• Diffusion methods in sub-Riemannian geometry.
• Random matrices and stochastic differential geometry,"

explains Fabrice Baudoin.

The project will fund three postdocs, three PhD students and several outreach and dissemination events.

The ERC Advanced Grant is one of the most prestigious European research grants, awarded to established researchers with an outstanding scientific track record. The grant provides up to €2.5 million over five years to support ambitious and groundbreaking projects across all fields of research. Read more about the grant here:

• https://erc.europa.eu/apply-grant/advanced-grant