Plenary lecture Benjamin Gess

Plenary lecture

Day 2 (Wednesday 23 April) @ 16:15 – 17:05

Benjamin Gess (TU Berlin and MPI Leipzig)

Fluctuations in Continuum

Fluctuations are ubiquitous in real world contexts and in key technological challenges, ranging from thermal fluctuations in physical systems to algorithmic stochasticity in machine learning and fluctuations driven by small-scale weather patterns in climate dynamics. At the same time, such complex systems are influenced by a multitude of factors, relying on a wide range of parameters and interactions. This motivates the exploration of scaling limits and continuum dynamics. A systematic understanding of such interplay of stochasticity, complex dynamical behaviour, and continuum limits seeks to reveal universal properties, irrespective of the specific details of the systems in question.

In this presentation we will examine the importance of modelling fluctuations in large systems through several examples, ranging from nonequilibrium thermodynamics to stochastic fluid dynamics and machine learning. We will demonstrate how their analysis uncovers deep connections between probabilistic features, partial differential equations with irregular coefficients, and geometric structures in the form of gradient flows on infinite dimensional manifolds.

Biography

Benjamin Gess pursued studies in Mathematics and Computer Science at the University of Bonn, obtaining his Master’s degree in Mathematics from the University of Warwick in 2008. He completed his doctorate in 2011 under the supervision of Michael Röckner at Bielefeld University, with a dissertation titled “Stochastic Flows Induced by Stochastic Partial Differential Equations”, as part of the International Research Training Group 1132. Following his PhD, he worked for two years as a postdoctoral researcher at TU Berlin and HU Berlin. He then spent a further two years at the University of Chicago on a research fellowship awarded by the German Research Foundation (DFG).

In 2015, he was granted a Max Planck Research Group, which he established at the Max Planck Institute for Mathematics in the Sciences in Leipzig, where he has served as group leader ever since. Concurrently, he held positions at Bielefeld University, initially as an associate lecturer and later as a temporary professor. In 2019, he was appointed full professor at Bielefeld University. Since 2024, he has held a chair at TU Berlin.

Benjamin Gess’s research focuses on stochastic partial differential equations, nonlinear partial differential equations, stochastic dynamics, interacting particle systems, machine learning, large deviation theory, and fluid dynamics.

In 2023, he was awarded an ERC Consolidator Grant, under which he is investigating fluctuations in the continuum and conservative stochastic partial differential equations. Since 2017, he has been a principal investigator in Collaborative Research Centre 1283, and since 2021, he has been a contributing scientist to the International Research Training Group 2235.