Date: 09/25, 16:0017:30 管理楼1308
Speaker: 李利平（湖南师范大学数学与统计学院）
Title: A brief introduction to representation stability theory
Abstract: Representation stability theory, introduced by Thomas Church and Benson Farb in 2010, explores the asymptotic behavior of a sequence of representations of groups (such as symmetric groups, general linear groups, etc.), and is widely applied to investigate properties of (co)homology groups of many important examples like configuration spaces, congruence subgroups, mapping class groups in geometric group theory, algebraic topology and algebraic geometry. Recently this theory was categorified via introducing some infinite discrete categories with particular combinatorial structure and stuying their representations. In this talk I will describe the motivation, background, current developent of this theory, as well as my own contribution. 
Date: 10/23, 16:0017:30 五教5406
Speaker: 刘晔（西交利物浦大学）
Title: Tutte多项式及其一般化
Abstract: Tutte多项式是拟阵的一个重要不变量。在超平面配置理论中，Tutte多项式包含了超平面配置的组合和拓扑信息。本次报告我们回顾这些结果，并介绍Moci的算术Tutte多项式在环面配置理论中的应用，以及LiuTranYoshinaga的GTutte多项式及其应用。 
Date: 11/6 ,16:0017:30 五教5406
Speaker: Yong Wei(USTC)
Title: Curvature flows of hypersurfaces and geometric inequalities
Abstract:Curvature flows of hypersurfaces are characterized by a family of hypersurfaces evolving in an ambient manifold with velocity determined by their extrinsic curvatures. The equations that arise are nonlinear parabolic differential equations. The curvature flows of hypersurfaces have many applications including the proof of some sharp geometric inequalities. In this talk, I will describe some recent work on this topic, with focus on the applications of curvature flows in the proof of isoperimetric type inequalities in Euclidean space and in hyperbolic space.

Date: 11/13 , 7：509：20 腾讯会议账号:950 391 9321 ; 密码112358
Speaker: Jiyuan Han(Purdue University)
Title: YauTianDonaldson conjecture for generalized KählerRicci soliton equations
Abstract:Let (X,D) be a log variety with an effective holomorphic torus action, and Θ be a closed positive (1,1)current. For any smooth positive function g defined on the moment polytope of the torus action, we study the MongeAmpere equations that correspond to generalized and twisted KahlerRicci gsolitons. We prove a version of YauTianDonaldson (YTD) conjecture for these general equations, showing that the existence of solutions is always equivalent to an equivariantly uniform Θtwisted gDingstability. When Θ is a current associated to a torus invariant linear system, we further show that equivariant special test configurations suffice for testing the stability. Our results allow arbitrary klt singularities and generalize most of previous results on (uniform) YTD conjecture for (twisted) KahlerRicci/Mabuchi solitons or KahlerEinstein metrics. This is a joint work with Chi Li.

Date: 11/20，7：509：20 腾讯会议账号:950 391 9321 ; 密码112358
Speaker: Charles Cifarelli (UC Berkeley)
Title: Shrinking gradient K\"ahlerRicci solitons and toric geometry
Abstract:Toric manifolds form an important class of complex manifolds with large symmetry. For compact manifolds, there is a wellknown procedure which exploits this symmetry to better understand invariant K\"ahler metrics. I will give a brief survey of these results on a compact manifold $M$ and then move on to study the situation when $M$ is noncompact, with an emphasis on understanding shrinking gradient K\"ahlerRicci solitons. There is a rich theory for such metrics in the compact setting, but the noncompact case is less well understood. In this talk, after providing some background, I will describe my recent work on the uniqueness of shrinking gradient K\"ahlerRicci solitons on noncompact toric manifolds. 
Date: 11/27,7：509：20 腾讯会议账号:950 391 9321 ; 密码112358
Speaker: Weiyong He(University of Oregon)
Title: Harmonic and biharmonic almost complex structures
Abstract:Harmonic almost complex structures was introduced by C. Wood in 1990s. We study the existence and regularity of weak harmonic almost complex structure from analytic point of view, as a tensorvalued version of harmonic maps.
We introduce the notion of biharmonic almost complex structures, in particular in dimension four. We prove that biharmonic almost complex structures are smooth, and there always exist an energyminimizing biharmonic almost complex structure.
Moreover, given a homotopy class, we prove existence results which depends on whether M is spin or not.
We also propose a conjecture that the homotopy class of energyminimizing biharmonic almost complex structures do not depend on a generic background metric. 
Date: 12/4,15:3017:00 五教5406
Speaker: Mao Sheng (USTC)
Title: Motivicity vs Periodicity
Abstract:In this talk I shall explain what the two notions in the title mean and why they should be important in algebraic geometry. 
Date: 12/4
Speaker: Lu Wang (California Institute of Technology)  online
Title: TBA
Abstract:TBA 
Date: 12/11
Speaker: Yuanqi Wang (University of Kansas)  online
Title: TBA
Abstract:TBA 