Zu Chongzhi Distinguished Lecture

Date and Time (China standard time): Monday, May 26, 10:00 am – 11:00 am

Location: WDR 1007

Zoom: 945 0257 3106, Passcode: dkumath

Title: Singularities in PDE

Speaker: Alexander Kiselev

Abstract: Partial differential equations (PDE) revolutionized science since the advent of calculus and serve as successful models to a staggeringly broad range of processes in nature and engineering.  Singularities in solutions of PDE are important since they often signify extreme phenomena or indicate a change in regime or breakdown of the model. I will overview some examples of singularity formation, with particular focus on fluid mechanics. 

Fluids are all around us, and we can witness the complexity and subtleness of their properties in every day life, in ubiquitous technology, and in dramatic events such as tornado or hurricane. There has been an enormous wealth of knowledge accumulated in the broad area of fluid mechanics, yet it is quite remarkable that many of the most fundamental and most important in applications questions remain poorly understood. In fact, Richard Feynman has called turbulence the greatest unsolved problem of classical physics, and one of the seven-million-dollar prize Millennium problems of Clay Institute is concerned with the possibility of singularities in the 3D Navier-Stokes equations – the foundational model of fluid mechanics.

In this talk oriented towards non-experts, I will in particular discuss the connection between these two challenges, as well as other key themes in fluids and PDE.

Bio: Alexander Kiselev received his BS degree from Saint-Petersburg State University in 1992, and his PhD from Caltech in 1997. After a postdoctoral position at MSRI he held positions at the University of Chicago, University of Wisconsin-Madison and Rice University. Since 2017, Kiselev is a William T. Laprade Distinguished Professor at Duke University.

Kiselev’s areas of expertise include mathematical quantum mechanics, reaction-diffusion equations, fluid mechanics, and mathematical biology . His research has been recognized by Sloan fellowship, NSF Career award, Guggenheim fellowship, Simons fellowship, as well as named lectures at the University of Oxford, University of Maryland, and Duke University. In 2018, Kiselev was an invited speaker at the PDE section of the International Congress of Mathematicians. He is currently serving as the managing editor of the Duke Mathematical Journal .