Taft Lectures

The Charles P. Taft Memorial Fund sponsors a program of public lectures each year, including one or more in mathematics. These lectures feature prominent mathematicians speaking on recent important developments in their field. Taft Lectures are aimed at a fairly general audience. Taft Lecturers sometimes also give a seminar talk which includes more specialized material. The name of each lecture under "Topic of Talk" below is a link to detailed information, including the date of each talk, the location, and the abstract. The Taft Lectures are free and open to the public.

The Department of Mathematical Sciences and the Taft Research Center welcome: 

Dr. Zhen-Qing Chen  

Professor of Mathematics

University of Washington

Tuesday, March 19, 2024

Baldwin Hall Room 544  


Heat kernel and transition density function  

Dr. Zhen-Qing Chen

There is a rich and fruitful interplay between analysis and probability theory. Transition density function of a Markov process is the fundamental solution, also called heat kernel, of its infinitesimal generator. In this talk, I will explain how probabilistic insights can help in the study of heat kernels in the context of rectilinear fractional Laplacians. These non-local operators are the infinitesimal generators of rectilinear α-stable processes, which are Levy processes on ℝd, whose coordinate processes are independent copies of one-dimensional α-stable processes. They have many distinct properties from that of isotropic fractional Laplacians. I will discuss the geometric characterization of an open subset D so that the Dirichlet heat kernels pD(t, x, y) on D are strictly positive. I will further present results on the properties of pD(t, x, y) including its regularity as well as the sharp two-sided bounds on C1,1-domain.


Refreshments will be served 3:15-3:45pm in the Math Faculty 
& Graduate Student Lounge Room 4118 French Hall West