Date: 05/07, 9:00-10:30 Online Zoom会议号92440013471；密码202104
Speaker: 张若冰,（Princeton University）
Title: 塌缩卡拉比-丘空间的度量几何
Abstract: 本报告的主题是爱因斯坦流形在体积塌缩时表现出的几何结构。我们集中讨论其中一个重要的特殊情形，即卡拉比-丘空间。这类空间为抽象的爱因斯坦流形展示了大量的可操作范例，并为几何和物理诸学科提供了深刻广泛的应用。卡-丘空间在演化过程中，其自身的复结构通常会出现退化现象，此过程会产生大量不可控的几何行为以及分析上的正则性丧失，这也导致了具体研究的各种本质性困难。以上过程在度量几何的表象是体积塌缩。我们将系统性展示卡-丘空间的塌缩极限，奇异几何的形成，以及尺度重构下爆破极限的丰富结构。 |
Date: 05/21, 9:00-10:30 Online 腾讯会议号31396184499；密码202104/物质科研楼C1124
Speaker: Jiangtao Yu（Lehigh University）
Title: Complete 2-convex translating solitons to the mean curvature flow in R^{n+1}
Abstract: By using a result of Derdziński on Codazzi tensors, we extend the work of Spruck and Xiao in "Complete Translating Solitons to the Mean Curvature Flow in R^3 with Nonnegative Mean Curvature" to higher dimensions. More precisely, for n ≥ 3, we show that n-dimensional complete 2-convex translating solitons for the mean curvature flow in Rn+1 are convex. |
Date: 05/25（周二）, 14:30-16:00 管理科研楼1418
Speaker: 曹阳（中国科学技术大学）
Title: 代数簇上有理点的稠密性
Abstract: 这是一个关于丢番图几何的科普报告，所讲的结果都是经典的结论。在这个报告中，我将通过包括三次超曲面和拟有理簇在内的一些经典的例子来展示代数几何工具如何被用来处理丢番图方程的解。 |
Date: 05/28, 10:00-11:30 物质科研楼C1124
Speaker: 吴加勇（上海大学）
Title: Geometric inequalities and applications in shrinkers
Abstract: In 2019, Yu Li and Bing Wang proved a sharp logarithmic Sobolev inequality in any shrinkers. In this talk, we will discuss some applications of this inequality in shrinkers, such as diameter estimates, dimension estimates of Schrodinger functions, Faber-Krahn inequalities, Rozenblum-Cwikel-Lieb inequalities, gap theorems, etc. |
Date: 05/28, 16:00-17:30 腾讯会议号: 572 283 2445；密码: 123456
Speaker: 梁兵兵 （苏州大学）
Title: From finite groups to sofic groups
Abstract: It is common to see that many nice dynamical invariants can be defined when the underlying acting group enjoys some nice approximation property, especially the amenability. In 1999, Gromov introduced a large class of groups named sofic groups, which unify the class of amenable groups and residually finite groups. In 2008, L. Bowen successfully generalized the measure entropy from the actions of amenable groups to the sofic groups. We will overview some recent development concerning the sofic groups. |
Date: 06/11（周五）, 10:00-11:30 腾讯会议号9289436801;密码444167 /物质科研楼C1124
Speaker: 方馨怡（华东师范大学）
Title: Semistable Vector Bundles on Rational Homogeneous spaces
Abstract: In the last decades, there has been a growing body of research on the stability of vector bundles on projective varieties. In this talk, I will introduce the crucial concept of stability of holomorphic vector bundles over P^n. In particular, the Grauert-Mulich-Barth theorem on projective spaces will be recalled. Furthermore, I will talk about the generalized Grauert-Mulich-Barth theorem on rational homogeneous spaces. This is based on a joint work with Rong Du and Yun Gao. |
Date: 06/18, 9:00-10:30 Zoom会议号：944 7203 2228；密码：202104
Speaker: Ovidiu Munteanu（University of Connecticut）
Title: Comparison results for three-dimensional manifolds
Abstract: Typical comparison results in geometry require information on Ricci curvature. In dimension three, we show that this can sometimes be relaxed to scalar curvature. An example is a sharp upper bound for the bottom spectrum of the Laplacian on noncompact three-dimensional manifolds. |
Date: 06/25, 10:00-11:30 物质科研楼C1124
Speaker: 胡京辰（上海科技大学）
Title: Local Regularity of Geodesics in the Space of Kahler Potentials
Abstract:The geodesic equation in the space of Kahler potentials is a homogenous complex Monge-Ampere equation. Because of the degeneracy, for a long time, the regularity of geodesics is limited to low order regularity. In a recent study, following an idea of Donaldson, we relate geodesic problems to Hamiltonian mechanics, and proved that, in some special region geodesic is $C^\infty$ smooth. |
Date: 07/02,10:00-11:30 物质科研楼C1124
Speaker: 陈丽娜 (南京大学）
Title: Segment inequality and almost rigidity structures for integral Ricci curvature
Abstract:We will show the Cheeger-Colding segment inequality for manifolds with integral Ricci curvature bound. By using this segment inequality, the almost rigidity structure results for integral Ricci curvature will be derived by a similar method as in \cite{CC1}. And the sharp H\"older continuity result of \cite{CoN} holds in the limit space of manifolds with integral Ricci curvature bound. |
Date: 07/09, 9:00-10:30 Tencent Meeting: 31396184499;Password：202104
Speaker: Brett Kotschwar(Arizona State University）
Title: Propagation of geometric structure under the Ricci flow
Abstract: We will discuss some unique-continuation results which ensure the propagation
of symmetry and other geometric features (e.g., warped product structures) forward and backward from a single time-slice
of a Ricci flow to the entire solution. We will then discuss some applications of these results to the classification problem for shrinking Ricci solitons. |
Date: 07/16,15:30-17:00， Zoom Meeting: 646 617 8889;Password:123456
Speaker: 伍晓磊(Bielefeld University）
Title: On the finiteness properties of groups (群的分类空间的有限性)
Abstract:We will start the talk with the basic notion of group and discuss the meaning of a group being finitely generated and finitely presented. We then discuss the natural high dimensional analog of these and give an overview on the finiteness properties of groups. In particular, we will highlight some major problems in the area. At the end, I will also discuss some of my own work related to finiteness properties of groups. Part of this is joint work with Rachel Skipper. |
Date: 07/19，周一， 下午 15:00-17:00 物质科研楼C1124
Speaker: 吴英毅 （中国科学院大学）
Title: HCMU metrics and isometric immersion problems
Abstract: HCMU metric is 1-dimensional non-CSC singular extremal Kahler metric. In this talk, we will first review the definition of HCMU metric and some important properties. Then we will focus on some isometric immersion problems related to HCMU metrics. |
Date: 07/23,10:00-11:30 物质科研楼C1124
Speaker: 宋基建 (天津大学应用数学中心）
Title: Irreducible cone spherical metrics and stable extensions of two line bundles
Abstract: Cone spherical metrics on compact Riemann surfaces are conformal metrics of constant curvature +1 with finitely many conical singularities. They are called irreducible if any developing maps of such metrics don't have monodromy in U(1). By using projective structures and indigenous bundles on compact Riemann surfaces, we construct a canonical surjective map from the moduli space of stable extensions of two line bundles to that of irreducible cone spherical metrics with cone angles in 2πZ. We also prove that the map is generically injective in algebro-geometric sense if the Riemann surface has genus ≥2. As an application, we obtain some new existence results about irreducible cone spherical metrics. This is a joint work with Lingguang Li and Bin Xu. |
Date: 07/30，10:00-11:30，物质科研楼C1124
Speaker: 张庆生 (北京大学)
Title: Applications of statistical physics methods to Gromov-Witten type theories
Abstract: Gromov-Witten type theory is a field theory coupled with two-dimensional topological gravity. The simplest example is the GW theory of a point which counts intersection numbers on the Deligne-Mumford moduli space and the famous Witten conjecture/ Kontsevich theorem establishes the relationship of this theory with KdV integrable hierarchy. The genus zero data of Gromov-Witten theory defines the quantum cohomology structure on the target manifold; the higher genus data can be packaged into some polynomials known as the finite generation structure conjecture. In this talk, i will give a brief introduction of GW theory and then introduce how to compute the GW invariants by renormalization theory and mean field theory. Some dualities between various GW type theories will be discussed from the point of view of the emergent geometry introduced by Jian Zhou. This talk is based on my joint works with Jian Zhou and Shuai Guo. |
Date: 08/06，10:00-11:30，物质科研楼C1124
Speaker: 汪永杰 (合肥工业大学)
Title: Harish-Chandra homomorphism for quantum superalgebras
Abstract: In this talk, we will review the Harish-Chandra homomorphism for Lie (super)algebras and quantum group. Then, motivated by Sergeev and Veselov's work, we establish a Harish-Chandra type theorem for quantum superalgebra $\mathrm{U}_q(\mathfrak{g})$ associated to a contragredient Lie superalgebra of type $A-G$, and obtain a set of basis for the center of $\mathrm{U}_q(\mathfrak{g})$. This is based on my recent work joint with Y. Luo and Y. Ye. |
Date: 08/13，9:00-10:30，腾讯会议号9503919321，会议密码112358/物质科研楼C1124
Speaker: 陈学渺 (University of Maryland, College Park)
Title: Singularities of Hermitian-Yang-Mills connections
Abstract: After introducing some background about stable bundles and HYM connections, I will explain both the analytic and algebraic sides when studying singularities of HYM connections. It turns out that local algebraic invariants can be extracted to characterize the analytic side. In particular, the analytic tangent cone is an algebraic invariant. (Based on joint works with Song Sun.) |
