Mathematics Class of 1960s Speaker, Prof. Mikolaj Sierzega, Cornell University

Mathematics Class of 1960s Speaker, Prof. Mikolaj Sierzega, Cornell University, Differential Harnack Bounds for Non-Local and Non-Linear Heat Flows, Friday, April 28, 1 – 1:45 pm, North Science Building 015, Wachenheim.

Abstract:  The classical heat equation is a beautiful, simple and immensely useful model of diffusion which – with due adjustments – may be found in a wide variety of scientific theories ranging from physics, through biology to finance.  The Li-Yau inequality, an instance of a so-called differential Harnack estimate, is a fundamental lower bound on the rate of decay of positive solutions.  In line with the canonical nature of the heat equation, the Li-Yau bound is a mathematical gem with powerful applications.  In this talk I will discuss some conceptual and technical challenges on the path to non-linear and non-local generalisations of the Li-Yau inequality and describe where such results may be put to good use.