Type: Seminar

Modified: Tue 24 May 2022 1353

Distribution: World

Expiry: 30 May 2022

Auth: miranda@120.17.37.145 (jluo0722) in SMS-SAML

Dear friends and colleagues,
## Webinar Speaker

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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

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•

•

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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

------

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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