TSVP Talk: "Fluctuations Across the Scales: Partial Differential Equations, Geometry and Noise" by Nicolas Dirr

Title: Fluctuations across the scales: Partial Differential Equations, Geometry and Noise

Speaker: Nicolas Dirr, Cardiff University

Abstract: Multi-scale analysis of physical systems  leads to “noisy” effective models on larger scales, i.e. deterministic (partial) differential equations perturbed by some small amount of randomness.  This noise is a feature, not a bug: there are situations where the remaining small noise  has visible effects on the macroscopic scale. Moreover the structure of the noise retains the memory of the smaller scales, so that  crucial information can be gained from this noise. The effective equations on the macroscale are not only themselves closely related to geometry (e.g. mean curvature flows), but the noise itself comes with a geometric structure: small fluctuations define “weights” on  tangent space, i.e. a thermodynamic metric.

Profile: Nicolas Dirr studied mathematics at the the universities of Tuebingen and Bonn in Germany with a year abroad in Cambridge/UK and obtained is Diploma in Mathematics in 1998 from Bonn, followed by a PhD from University of Leipzig/Germany in 2002 under supervision of Prof. Stephan Luckhaus. After postdoctoral positions at the University of Texas at Austin and the Max-Planck-Institut for Mathematics in the Sciences (Junior research group leader), he went as lecturer to Bath, UK and then as Reader and from 2016 Professor to the University of Cardiff, Wales, UK.
His research interest lies at the interface of nonlinear partial differential equations and stochastic processes. His research is in pure mathematics but motivated by modelling real world systems. This includes scaling limits of interacting particle systems, fluctuating hydrodynamics, geometric evolution equations, homogenization, control problems and mean field games, gradient flows and, recently, models for the visual cortex.
 

Language: English

Target audience: General audience/everyone at OIST and beyond.
Freely accessible to all OIST members and guests without registration.

This talk will also be broadcast online via Zoom:
Meeting ID: 993 1216 5065
Passcode: 603487

※ Please note that this event may be recorded and the videos uploaded. In addition, photos may be taken during the event. These are intended for publication online (the OIST website, social media, etc.)※