Week of Events
Analysis seminar: Lawford Harrison (Indiana)
Title: The hot-cold distance Abstract: Given a solution to the heat equation on a Euclidean domain, Riemannian manifold, or discrete graph, it is natural to ask where the hottest and coldest points are located over large time scales. Rauch's hot spots conjecture states that, in the Euclidean setting with Neumann boundary conditions, these points should all tend […]
Math Physics Seminar: Kevin Dembski (Duke University)
Title: Singularity Formation in the Incompressible Porous Medium Equation without Boundary Mass Abstract: In this talk, I will discuss recent work on the problem of singularity formation in the incompressible porous medium (IPM) equation. We construct Lipschitz continuous solutions of the IPM equation which vanish on the boundary of the domain and blow-up in finite […]
Geometric analysis seminar: Xingyu Zhu (朱星宇)
Title: from Cones to cylinders: asymptotic geometry of Ricci flat manifolds with linear volume growth. Abstract: The uniqueness of infinity plays a crucial role in understanding solutions to geometric PDEs and the geometric/topological properties of manifolds with Ricci curvature lower bounds. A major progress is made by Colding—Minicozzi who studied one type of infinity, called the asymptotic cones, […]
Special Data Science Seminar: Ruiyu Han
Title: Convergence of a Sequential Monte Carlo algorithm towards multimodal distributions.Abstract: We study a sequential Monte Carlo (SMC) algorithm to sample from the Gibbs measure with a non-convex energy function at a low temperature. Sampling from multimodal distributions is a challenge that the classical algorithms become extremely slow, for example, the time complexity of obtaining good […]