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

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 talk, I will first briefly reflect on this seminal relation between
(gradient-flow) variational structures and large deviations.  I will then focus on using
these structures to study asymptotic limits in certain (non-gradient-flow) PDEs.
Specifically, I will present these connections for the underdamped Langevin
Fokker-Planck equation and focus on the (singular) overdamped limit of this degenerate
PDE.

https://url.au.m.mimecastprotect.com/s/-KVVCGv0oyCAEP1WMtKfRfBiJgs?domain=unsw.zoom.us
Meeting ID: 83425275881
Password: 041345