Geometry and Analysis Colloquium

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Past Schedule

• 题目 Title:	关于四维 Yang-Mills 连络的爆破分析
  报告人 Speaker:	殷浩
  单位 Affiliation:	中国科学技术大学
  时间 Datetime:	2022-10-17 14:00 -- 15:30
  地点 Venue:	腾讯会议：678-905-872
  摘要 Abstract:	报告四维流形上能量有界的杨-米尔斯(Yang-Mills)连络的爆破现象。通过在杨-米尔斯联络的能量集中点附近的脖子区域上选择合适的规范，研究连络形式的渐近展开，由此证明弱极限连络和泡泡联络之间的一个曲率等式。进一步启发了杨-米尔斯场等相关几何偏微分方程的紧性现象的研究。
  个人简介 Personal Profile:	殷浩，中国科学技术大学数学科学学院副教授。主要从事调和映射和 Yang-Mills 联络相关问题的紧性研究。主持国家自然科学基金科研项目4项。在J. Funct. Anal., Calc. Var. Partial Differential Equations, Comm. Anal. Geom. 等国际知名杂志上发表研究论文十余篇。

• 题目 Title:	Signature and Toledo invariants for flat unitary bundles over surfaces with boundary
  报告人 Speaker:	万学远
  单位 Affiliation:	重庆理工大学
  时间 Datetime:	2022-07-14 09:30 -- 11:00
  地点 Venue:	Tencent Meeting ID: 616-496-230 Passcode:202207
  摘要 Abstract:	This talk deals with the representations of the fundamental groups of compact surfaces with boundary into classical simple Lie groups of Hermitian type. We relate work on the signature of the associated local systems, due to Meyer and Atiyah, to Burger-lozzi-Wienhard’s Toledo invariant. To measure the difference, we extend Atiyah-Patodi-Singer’s rho invariant, initially defined on U(p), to discontinuous class functions, first on U(p,q), and then on other classical groups via embeddings into U(p,q). This work is joint with Prof. Inkang Kim and Prof. Pierre Pansu.
  个人简介 Personal Profile:	万学远博士，重庆理工大学数学科学研究中心特聘教授。2016 年博士毕业于南开大学，2017- 2021 年先后在瑞典查尔姆斯理工大学和韩国高等研究院做博士后。目前主要从事复几何的相关研究，研究结果发表在 JMPA, JAG, Compositio, Tran. AMS, Math. Ann. 等国际著名数学期刊。

• 题目 Title:	Analysis of Yang-Mills-Higgs-Dirac model
  报告人 Speaker:	吴瑞军
  单位 Affiliation:	北京理工大学
  时间 Datetime:	2022-07-05 09:00 -- 10:30
  地点 Venue:	Tencent Meeting ID: 289-224-876 Passcode: 202207
  摘要 Abstract:	We will describe a nonlinear model involving the sigma models and the gauge theory. This can be seen as a gauged Dirac-harmonic map model, which will be located on a fiber bundle with compact fibers. After a description of the model, we emphasize on the blowup analysis and the bubbles.
  个人简介 Personal Profile:	吴瑞军，北京理工大学教授，获中科院数学与系统科学研究院以及Max-Planck研究所双博士学位。先后在Max-Planck、De Giorgi Center of SNS、 SISSA从事博士后研究工作。主要研究兴趣为与Dirac算子有关的变分问题和方程。相关研究工作发表在Comm. Math. Phys. , Trans. AMS., Calc. Var. PDE., J. Differential Equations, J. Geom. Phys., 等杂志上。

• 题目 Title:	Transverse \(\mathcal{F}\) entropy for Riemannian foliations and its application
  报告人 Speaker:	Dexie LIN
  单位 Affiliation:	College of Mathematics and Statistics of Chongqing University
  时间 Datetime:	2022-06-29 10:00 -- 11:30
  地点 Venue:	Tencent Meeting ID: 520-642-524 Passcode: 202206
  摘要 Abstract:	In this talk, we introduce some basic notions of Riemannian foliations and given an entropy functional on Riemannian foliation, we also give some properties of this functional. In application, we give a necessary condition for codimension 4 Riemannian foliation admitting the transverse Einstein metric by using the entropy and basic Seiberg-Witten equations.
  个人简介 Personal Profile:	Dexie LIN, who got the Ph.D of The University of Tokyo in 2020 September. His main interest is about the Seiberg-Witten equations and low dimensional manifold geometry. The related results are published on Proc. Amer. Math. Soc. and Topology Appl. etc.

• 题目 Title:	Topics in the uniqueness of floating bodies
  报告人 Speaker:	张宁
  单位 Affiliation:	华中科技大学
  时间 Datetime:	2022-06-23 09:00 -- 10:30
  地点 Venue:	Tencent Meeting ID: 825-526-905 Passcode: 202206
  摘要 Abstract:	In this talk, I will present a couple of recent results related with the uniqueness of floating bodies.
  个人简介 Personal Profile:	张宁，华中科技大学副研究员，博士生导师。2017 年毕业于加拿大阿尔伯塔大学获博士学位，美国国家数学科学研究所博士后，肯特州立大学博士后。主要研究领域涵盖凸几何、几何分析、黎曼几何和概率相关方向。部分成果发表在 Trans. Amer. Math. Soc., J. Func. Anal., CVPDE 等学术期刊上。

• 题目 Title:	Regularity of subelliptic harmonic maps with values into metric spaces of nonpositive curvature
  报告人 Speaker:	桂耀挺
  单位 Affiliation:	Max Planck Institute for Mathematics in the Sciences
  时间 Datetime:	2022-06-21 15:00 -- 16:30
  地点 Venue:	Tencent Metting ID: 590-939-207 Passcode: 202206
  摘要 Abstract:	We present a result of Holder continuity of a harmonic map from a domain of a sub-Riemanian manifold into a locally compact manifold with nonpositive curvature, and more generally into a non- positively curved metric space in the Alexandrov sense. This is a joint work with Prof. Jost and Prof. Li-Jost.
  个人简介 Personal Profile:	Gui Yaoting, obtain his doctorate degree from USTC in June 2022. His main interest is nonlinear analysis on manifolds, especially in the analysis on singular space, such as conical manifolds and degen- erate elliptic operator. He visits the Max Planck Institute from 2022.03 to 2022.07, and he has been offered a postdoc fellowship in BICMR.

• 题目 Title:	A Liouville’s theorem for some Monge-Ampère type equations
  报告人 Speaker:	韦韡
  单位 Affiliation:	南京大学
  时间 Datetime:	2022-06-21 08:30 -- 10:00
  地点 Venue:	Tencent Meeting ID: 807-884-844 Passcode: 202206
  摘要 Abstract:	In this talk we study a Monge-Ampère type equation that interpolate the classical 2-Yamabe problem in conformal geometry and the 2-Hessian equation in dimension 4.This is a joint work with Hao Fang and Biao Ma.
  个人简介 Personal Profile:	韦韡，现南京大学助理研究员。博士毕业于中国科学技术大学，上海数学中心博士后。曾获得博士后创新人才计划。在 Adv.Math, J.Funct. Anal., Calc. Var.等杂志发表过文章。