Fractional Parabolic Theory as a High-dimensional Limit of Fractional Elliptic Theory

Explore a mathematical physics lecture on "Fractional Parabolic Theory as a High-dimensional Limit of Fractional Elliptic Theory" presented by Mariana Smit Vega Garcia from Western Washington University at the Institute for Advanced Study. Delve into the fascinating connections between elliptic and parabolic theory of partial differential equations, with particular focus on how elliptic theory represents the steady-state version of parabolic theory. Discover how parabolic estimates can yield elliptic statements by eliminating the time parameter, while learning about the more complex challenge of deriving parabolic statements from elliptic ones. The 51-minute talk introduces a high-dimensional limiting technique that proves theorems about solutions to the fractional heat equation from their elliptic counterparts. This presentation, part of the Analysis and Mathematical Physics series, represents joint work with Blair Davey and will take place on March 25, 2025, at Simonyi Hall 101 with remote access available.