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Geometry and Dynamics of Phase Transitions in Periodic Media

Analysis, Dynamics, and Applications Seminar

Geometry and Dynamics of Phase Transitions in Periodic Media
Series: Analysis, Dynamics, and Applications Seminar
Location: Online
Presenter: Raghav Venkatraman, Department of Mathematical Sciences, Carnegie Mellon University

In this talk we discuss recent progress on homogenization of the Allen-Cahn equation in a periodic medium to Brakke's formulation of anisotropic mean curvature flow. The starting point of our work is the recent Gamma-convergence result of Cristoferi-Fonseca-Hagerty-Popovici, and we combine it with the Sandier-Serfaty scheme for the convergence of gradient flows. Along the way, our analysis also provides resolution to a long-standing open problem in geometry: what do distance functions to planes look like, in periodic Riemannian metrics on $R^n$ that are conformal to the Euclidean one? The corresponding question about distance functions to points, has a long history that goes back to Gromov and Burago.  This represents joint work with Irene Fonseca (CMU), Rustum Choksi and Jessica Lin (McGill). 

Zoom: https://arizona.zoom.us/j/99410014231
Password: “arizona” (all lower case)