Speaker: Gideon Simpson, Drexel University
Title: Nonlocal Diffusions with Additive Noise
Abstract: In this talk I will discuss recent work on infinite dimensional nonlocal diffusions with additive noise. These may be obtained as the continuum limits of noise driven Kuramoto oscillator systems. A well-posedness theory is developed for this infinite dimensional problem, and convergence results are obtained for both the associated semi-discrete and fully discrete problems. This provides a basis for studying the associated metastability problems of the continuum limit Kuramoto system, which may also be viewed as an approximation of a high, but finite, dimensional problem. Ongoing progress on studying the metastability, both numerically and analytically will be presented. Novel challenges in the analysis are also highlighted. This work is in collaboration with Georgi Medvedev (Drexel).