"Diffusion processes on rough spaces and random geometric models"
Abstract: Mathematical models in physics, biology, engineering, material sciences and social media are usually developed to understand structures and phenomena of high complexity. The more realistic a model is, the more “roughness” we expect to find. Introducing randomness allows us to treat richer, more complicated situations. In this talk I will outline how my research in analysis and probability aims to gain a better understanding of these structures: On the one hand, studying the stochastic processes intrinsic to a certain space can also reveal geometric and analytic information about it. On the other hand, the geometric properties of random sets and the asymptotic behavior of associated functionals are key in the development of statistical tools to analyze spatial data.
Host: Brett Wick