Joint USYD-UNSW Seminar on Stochastic PDEs: Upanshu Sharma (UNSW) -- Can the behaviour of microscopic stochastic systems give insight into analysis of upscaled PDEs (part 3)?

Zoom link: https://unsw.zoom.us/j/83425275881?from=addon
Meeting ID: 83425275881
Password: 041345

Rigorous proofs of singular limits in evolution equations is a hard problem in general,
although some fields, for instance singular limits in ODEs and homogenisation theory,
are well developed.  Starting from the seminal work of Felix Otto and co-authors, it has
become evident that a large class of evolution equations (specifically gradient flows)
have a natural variational structure which is well-suited for rigorous asymptotic
analysis.  Furthermore, over the last decade it has become clear that there are deep
connections between these (gradient-flow) variational structures and large-deviations of
underlying stochastic particle systems.  

In this part 3, I will explore the utility of large-deviations in dealing with singular
limit problems in a certain class of (possibly nonlinear) Fokker-Planck equations.  The
key approach is to study the (Gamma-)convergence of the large-deviation rate
functionals, which in addition to convergence of solutions also provide convergence of
fluctuations.