Advances in Applied Mathematical Analysis and Numerical Methods: Ten Years of CoLab
2018-11-05 — 2018-11-08
@ The University of Texas at Austin
The UT Austin | Portugal CoLab Program in Applied Mathematics has been running for 10 years now. It has been remarkably successful in promoting research collaboration and providing mobility opportunities for faculty members, as well as in hosting doctoral and post-doctoral students, especially in the field of applied PDEs. The meeting Advances in Applied Mathematical Analysis and Numerical Methods: Ten Years of CoLab brings together many of the researchers who have been directly or indirectly involved in the program, to report on recent achievements while paving the way for future collaborations. Topics covered range from the analysis of PDEs to more computational aspects and applications in Science and Engineering.
Mini-course on Hydrodynamic limit of particle systems on resistance spaces
2019-01-25 — 2019-02-06
The goal of the mini-course by Joe Chen is to describe the recent progress on establishing scaling limits of many-particle systems on state spaces which are bounded in the resistance metric, a.k.a. "resistance spaces." These include trees, fractals, and random graphs arising from critical percolation. As a concrete example, one can establish scaling limits of the weakly asymmetric exclusion process on the Sierpinski gasket interacting with 3 boundary reservoirs, which generalizes (in a nontrivial way) the analysis on the unit interval interacting with 2 boundary reservoirs.
The key ideas behind these results will be explained, and connections to the analysis of (S)PDEs, and issues of non-equilibrium statistical physics, on resistance spaces will be discussed. From a technical point of view, some novel functional inequalities for the exclusion process that relates to electrical resistance will be addressed, and the way they are used to effect "coarse-graining" in passing to the scaling limits will be described.
