Geometric Analysis Seminar

Building 2, 131

Speaker: Pei-Ken Hung (University of Illinois at Urbana-Champaign)Title: Thom's gradient conjecture for geometric PDEsAbstract:Understanding solutions near their singularities is a fundamental topic in PDE. The pioneering works of Leon Simon established the uniqueness of blow-ups for a broad class of geometric PDEs. Subsequently, the investigation of higher-order behavior becomes a crucial step for further analysis. In this talk, we will provide a complete description of the second-order asymptotic based on analytic gradient flows. As a consequence, we verify Thom's gradient conjecture in the context of geometric PDEs. This talk is based on joint work with B. Choi.