SMS scnews item created by Miranda Luo at Tue 24 May 2022 1303
Type: Seminar
Modified: Tue 24 May 2022 1353
Distribution: World
Expiry: 30 May 2022
Calendar1: 30 May 2022 1500-1600
CalLoc1: Zoom webinar
Auth: miranda@120.17.37.145 (jluo0722) in SMS-SAML

# Blowup solutions and vanishing estimates for singular Liouville equations

### Lei Zhang

Dear friends and colleagues,

on Monday, 30 May 2022 at
01:00 PM for Beijing, Hong Kong and Perth
02:00 PM for Seoul and Tokyo
03:00 PM for Canberra, Melbourne and Sydney
05:00 PM for Auckland

Professor Lei Zhang is giving a talk in our Asia-Pacific Analysis and PDE Seminar on

Blowup solutions and vanishing estimates for singular Liouville equations

Abstract:

The singular Liouville equation is a class of second order elliptic partial differential equations defined in two dimensional spaces: $\Delta u+ H(x)e^{u}=4\pi \gamma \delta_0$ where $$H$$ is a positive function, $$\gamma>-1$$ is a constant and $$\delta_0$$ stands for a singular source placed at the origin. This deceptively simply looking equation has a rich background in geometry, topology and Physics. In particular it interprets the Nirenberg problem in conformal geometry and is the reduction of Toda systems in Lie Algebra, Algebraic Geometry and Gauge Theory. Even if we only focus on the analytical aspects of this equation, it has wonderful and surprising features that attract generations of top mathematicians. The structure of solutions is particularly intriguing when $$\gamma$$ is a positive integer. In this talk I will report recent joint works with Juncheng Wei that give a satisfactory answer to important issues to this equation. I will report the most recent results, new insights, and the consequences of these results.

Chair: Ki-Ahm Lee (Seoul National University, South Korea)

More information and how to attend this talk can be found at the seminar webpage .

Miranda
On behalf of Daniel H. and Ben

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## Webinar Speaker

Lei Zhang
Professor @ University of Florida, United States

Professor Lei Zhang got his PhD from Rutgers University in 2001 under the supervision of Yanyan Li. After that he was employed at Texas A&M, University of Alabama-Birmingham and University of Florida. theory.

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