Uploaded May 2026 | Updated September 2026, 2 weeks ago
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.
Find out more about the TSVP on the program website: oist.jp/visiting-program
#OIST #OIST-TSVP #Theoretical #Science #VisitingProgram #Okinawa #TSVP #NicolasDirr #PartialDifferentialEquations #Geometry #Noise #MultiScaleAnalysis #MeanCurvatureFlow
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.
Find out more about the TSVP on the program website: oist.jp/visiting-program
#OIST #OIST-TSVP #Theoretical #Science #VisitingProgram #Okinawa #TSVP #NicolasDirr #PartialDifferentialEquations #Geometry #Noise #MultiScaleAnalysis #MeanCurvatureFlow
