UTK-PDE Distinguished Lecture Series is a series of lectures in partial differential equations (PDEs) delivered virtually by world renowned mathematicians. Each part in the series consists of three to five lectures covering core ideas, techniques, and state of the art in selected topics in the area of partial differential equations. Lectures will be thoughtfully designed and technically simplified so that they will be accessible to an audience with only basic background in Analysis and PDEs. All lectures will be recorded and posted together with lecture notes (Youtube Channel UTK-PDE Lecture Series). The series is founded and organized by Dr. Tuoc Phan with the support from the Department of Mathematics at the University of Tennessee - Knoxville.

Volume I (Fall 2020): Professor Ovidiu Savin (Department of Mathematics, Columbia University).

Professor Savin
Brief Biography: Ovidiu Savin received his Ph.D. in mathematics from the University of Texas at Austin in 2003. He was a Miller Postdoctoral Fellow at UC Berkeley from 2003-2006, an associate professor at Columbia University from 2006-2011, and then the full professor there since 2011. Professor Savin's research is in partial differential equations. He is well-known for his affirmative resolution of the De Giorgi's conjecture, and for the result on the continuity of the gradients of solutions to the infinity-Laplacian equation in two dimensions. Together with his collaborators, Professor Savin has obtained many ground-breaking results on the smoothness of solutions of the Monge-Ampère equation, and of Monge-Ampère eigenfunctions. Other significant results of Professor Savin include a construction of singular minimizers in low dimensions, and theory of nonlocal minimal surfaces. Professor Savin was an invited speaker at the International Congress of Mathematicians (ICM 2006, Madrid, Spain). He has been recognized by many prestigious awards and honors including the Sloan Fellowship (2007-2009), and the Stampacchia Medal in 2012. Professor Savin is an editor of many leading mathematics journals such as Advances in Mathematics, and Calculus of Variations and Partial Differential Equations. Additional information about Professor Savin can be found in this Wikipedia page and in his [CV].

Title: The Monge-Ampère equation

Abstract: The Monge-Ampère equation plays an important role in many areas of mathematics like geometry, fluid mechanics, optimization etc. I will give an overview of the classical regularity theory for this equation. I will discuss the theory of weak solutions introduced by Alexandrov, Caffarelli's interior estimates, partial regularity, and some applications to the Minkowski problem and to optimal transportation.

Volume I Flyer [PDF]. Sharing the flyer and the series information is greatly appreciated.

Schedule (Zoom information/passcode will be available 30 minutes before each lecture)

Date/TimeZoom information Lecture Notes Lecture Videos
October 29, 2:50PM (EDT) Zoom link, Passcode: 980817 Lecture 1 Video 1
November 5, 2:50PM (EST) Zoom link, Passcode (not required) Lecture 2 Video 2
November 12, 2:50PM (EST) Zoom link, Passcode (not required) Lecture 3 Video 3
November 19, 2:50PM (EST) Zoom link, Passcode (not required) Lecture 4 Video 4

Youtube Channel: UTK-PDE Lecture Series. Feel free to subscribe.

Contact information: Write to Tuoc Phan at phan(at)math(dot)utk(dot)edu if you would like to receive the reminding messages on this event or if you have questions/requests.