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为贯彻落实教育部关于教育教学改革系列“101计划”,进一步推进数学学科人才培养改革,加强几何方向核心课程建设,2024年6月1日,“101计划”几何课程研讨会在中国科学技术大学举办。
Nonlinear potential theory and elliptic regularity theory are two classical topics in the modern analysis of partial differential equations. In this talk I show how these themes merge to solve the lon...
This lecture concerns the metric Riemannian geometry of Einstein manifolds, which is a central theme in modern differential geometry and is deeply connected to a large variety of fundamental problems ...
We investigate the frame set of regular multivariate Gaussian Gabor frames using methods from Kahler geometry such as Hormander's $\dbar$-L2 estimate with singular weight, Demailly's Calabi--Yau metho...
We consider the Cauchy problem for the defocusing cubic NLS on R3T1 and establish almost sure scattering for random initial data. The main obstacle to extend the classical almost sure scattering resul...
In this talk, I will give a survey of results related to the problem of computing Hausdorff dimension of various dynamically defined sets, such as singular vectors. The aim is to try to describe the l...
In this talk, we shall review firstly the study history of Kazdan-Warner equations on compact Riemann surfaces, which was proposed by Kazdan and Warner on Annals of Math on 1974. Then we shall show th...
The logarithmic Brunn-Minkowski inequality conjecture is one of the most intriguing challenges in convex geometry since 2012. Notably, this conjectured inequality is stronger than the celebrated Brunn...
This talk first solves explicitly a Riemann-Hilbert problem of confluent hypergeometric systems. It then conjectures and proves a special case that the WKB approximation of the monodromy data of confl...
In this talk, we report several very recent asymptotic results on certain classical geometric quantities viewed as random variables on the moduli space of Riemann surfaces for large genus (and many cu...
Rigid local systems over algebraic curves are those local systems determined by their local monodromies. They include many important classical local systems, such as those obtained from Bessel equatio...
We study mean curvature flows (MCFs) coming out of cones. As cones are singular at the origin, the evolution is generally not unique. A special case of such flows is known as the self-expanders. We wi...
Discuss [Bha, §3.1-3.3]. Please cover §3.1 and §3.3. You can recall/admit materials in §3.2 for some discussions in §3.3.
In this talk I will recall Richberg's extension theorem of plurisubharmonic functions and discuss its application in Kahler geometry.
Mean curvature flow is the fastest way to decrease the area of surfaces. It is the model in many disciplines such as material science, fluid mechanism, and computer graphics. The translators are a spe...

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