# UTK-PDE DISTINGUISHED LECTURE SERIES

### University of Tennessee - Knoxville

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 II (Spring 2021): Professor Jun-cheng Wei (Department of Mathematics of University of British Columbia). Enter your name and e-mail address in this form if you would like to receive reminding messages.

Brief Biography: Juncheng Wei received his Ph.D. in mathematics from the University of Minnesota in 1994. From 1994-1995, he stayed in SISSA (Italy) as a postdoc. He then came to Chinese University of Hong Kong as an assistant professor from 1995-1999, then an associate professor from 1999-2003, and a chair professor in mathematics from 2003-2009. Professor Juncheng Wei moved to University of British Columbia in 2009, and currently he is a full professor and Canada Research Chair (Tier I) there. Professor Wei has published more than 450 peer reviewed articles and many of them are in top mathematics journals such as Advances in Mathematics, Annals of Mathematics, Communication in Pure Applied Mathematics, Journal für die reine und angewandte Mathematik (Crelle's Journal). Professor Wei is well-known for his outstanding results in constructing special classes of solutions in problems on concentration phenomenon in Nonlinear PDEs, De Giorgi conjectures, phase transitions, singular perturbation problems, mean curvature flows, harmonic map flows, and many others. Professor Wei has been recognized by many prestigious awards and honors including the Silver Morningside Medal in 2010, the CMS Jeffery-Williams Prize and Simons Fellow in Mathematics in 2020. Professor Wei was an invited speaker at the International Congress of Mathematicians (ICM 2014). In 2018, professor Wei was also listed as an ISI Highly Cited Researcher. Professor Wei is currently a Fellow of Royal Society of Canada (FRSC). He also serves as an editor of many leading mathematics journals including Journal of Functional Analysis, Journal of Differential Equations, Transactions of London Mathematical Society. Additional information about Professor Wei can be found in this Wikipedia page and in his [CV].

Title: Gluing methods and Applications.

Abstract: In this lecture series, I will introduce the gluing methods and applications. Four examples of nonlinear equations will be used to illustrate the methods: 1) nonlinear Schrödinger equations (finite dimensional reduction method) 2) Allen-Cahn equation and minimal surfaces (infinite dimensional reduction method) 3) energy-critical parabolic equations (parabolic gluing method) 4) 2D Euler equation (gluing method applied to transport equation). If time permits I will also describe some applications of the reverse gluing methods including $C^{2,\alpha}$ estimates for interfaces of Allen-Cahn and non-existence of Type II blow-ups for energy-critical heat equation.

Schedule: Zoom link will be available 30 minutes before each lecture. Enter your name and e-mail address in this form if you would like to receive reminding messages.

Date/TimeZoom information Lecture Notes Lecture Videos
April 1, 2:50PM (EDT) Zoom link Lecture Slides Lecture 1
April 8, 2:50PM (EST) Zoom link Lecture Slides Lecture 2
April 15, 2:50PM (EST) Zoom link Lecture Slides Lecture 3
April 22, 2:50PM (EST) Zoom link Lecture Slides Lecture 4
April 29, 2:50PM (EST) Zoom link Lecture Slides Lecture 5

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

# Past Events:

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

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.