During the last ten years we have discovered a tight link between gradient flows on one hand and large deviations on the other. Gradient flows are a class of dynamical systems: evolution equations driven by the 'fastest decrease’ of an energy or entropy functional. Large deviation theorems give rigorous asymptotic characterizations of rare events of random variables.
These two unlikely bedfellows turn out to be closely related, in the case of evolution equations that arise as macroscopic, upscaled limits of stochastic processes. Such evolution equations arise in many physical processes: diffusion, heat conduction, fluid flow, elasticity, plasticity, chemical reactions, and many more. In this talk I will show how these two concepts relate to each other and to the underlying physics, chemistry, or biology. I also will show how it leads to a rigorous underpinning of a modelling methodology known as Variational Modelling, and in this way gives rise to new descriptions of the physical world around us.
Bio: Mark Peletier obtained an MSc in mathematics from Leiden University (cum laude), and a Diplôme d'Études Approfondies at the Laboratoire d'Analyse Numérique (now Laboratoire Jacques-Louis Lions) of Université Paris VI, both in 1992. He received his PhD at Leiden University (1997), and continued to work at the University of Bath (1997-1998) and the Centre for Mathematics and Computer Science in Amsterdam (1998-2004) before becoming a full professor in mathematics at the Technische Universiteit Eindhoven. His research interest focuses on differential equations and their applications to real-world systems. His work spans the spectrum from applied to fundamental, with mathematical contributions to biology, geology, chemistry, pattern formation, solid mechanics, fluid dynamics, and contributions to the theory of variational calculus and differential equations. Peletier received a VIDI grant in 2003, a VICI grant in 2011, and was a member of De Jonge Akademie from 2006 to 2011. He was visiting professor in London (2000), Bath (2007, 2010-11) and Vancouver (2008), and he serves on the editorial board of three international journals.