Geometric Analysis seminar talk list:
1.
Time:14:00-15:00, Wednesday, October 12
Speaker:Jianchun Chu, Peking University
Title:The solvability of hypercritical deformed Hermitian-Yang-Mills equation
Abstract:In this talk, Dr Chu will introduce the notions of coerciveness and properness of the J-functional on the space of almost calibrated (1,1)-forms and show that they are both equivalent to the existence of solutions to the hypercritical deformed Hermitian-Yang-Mills equation. This is a joint work with Man-Chun Lee.
ZOOM ID：828 0806 0395
Password：005267
2.
Time:9:00-10:00, Thursday, October 20
Speaker:Xin Fu, University of California, Irvine
Title:Uniqueness of Tangent Cone of Kahler Einstein Metrics on Singular Varieties with Crepant Singularities
Abstract:Let (X,L) be a polarized Calabi Yau variety (or canonical polarized variety) with crepant singularity. Suppose ωKE∈c1(L) (or ωKE∈c1(KX)) is the unique Ricci flat current (or Kahler Einstein current with negative scalar curvature) with local bounded potential constructed. By E-G-Z, we show that the local tangent at any point p∈X of metric ωKE is unique.
ZOOM ID：815 4288 5374
Password：045752
3.
Time:14:00-15:00, Wednesday, October 26
Speaker:Jiaxiang Wang, BICMR
Topic:紧Kahler流形上p-Nash entropy有界的度量的半径和体积估计
Abstract:Guo-Phong-Song-Sturm在arXiv:2209.09428的文章里证明了紧Kahler流形上满足p-Nash entropy有界并且退化性满足一定限制的度量半径有一致上界，单位球体积有一致下界。作为应用可以推出沿着Kahler Ricci Flow的一些一致估计。本次讨论班报告人准备报告这篇文章。
ZOOM ID：871 4526 1242
Password：003808
4.
Time:14:00-15:00, Wednesday, November 2
Speaker:Jiyuan Han, ITS
Title:Maximal degeneration of symmetric Calabi-Yau hypersurfaces
Abstract:In this study seminar, I will report the recent work by Hultgren-Jonsson-Mazzon-McCleerey. The talk will focus on the Real Monge-Ampere equation on essential skeletons.
ZOOM ID：826 2138 0433
Password：691050
5.
Time:14:00-15:00, Wednesday, November 9
Speaker:Shih-Kai Chiu, University of Oxford
Title:Nonuniqueness of Calabi-Yau metrics with maximal volume growth
Abstract:Conlon-Rochon, Y. Li and Szekelyhidi independently constructed the first examples of Calabi-Yau metrics on C^n with maximal volume growth and singular tangent cones at infinity. In this talk, I will discuss a new family of Calabi-Yau metrics on C^3 asymptotic to C x A2, where A2 is the two dimensional A2 singularity equipped with the flat cone metric. These metrics are distinct in the sense that any two of them are not related by scaling and isometry. I will also discuss a refinement of a conjecture of Szekelyhidi about the classification of such metrics.
ZOOM ID：880 3418 8645
Password：563630
6.
Time:9:00-10:00, Thursday, November 17
Speaker:Peng Zhou, University of California Berkeley
Title:Microlocal sheaf theory and Toric Homological Mirror Symmetry
Abstract:Homological Mirror Symmetry (HMS) is an equivalence of categories, where one category (B-side) involves complexes of coherent sheaves, and the other side (A-side) involves Lagrangians. In some nice cases, the A-side space can be described in a combinatorial way, using microlocal sheaves living on a skeleton. I will give some examples to show how things works when the B-side is a toric variety.
ZOOM ID：844 2784 4751
Password：251346
7.
Time:9:00-10:00, Thursday, December 1
Speaker:Yi Lai, Stanford University
Title:O(2)-symmetry of 3D steady gradient Ricci solitons
Abstract:For any 3D steady gradient Ricci soliton with positive curvature, if it is asymptotic to a ray we prove that it must be isometric to the Bryant soliton. Otherwise, it is asymptotic to a sector and called a flying wing. We show that all flying wings are O(2)-symmetric. Hence, all 3D steady gradient Ricci solitons are O(2)-symmetric.
Tencent Meeting:422 762 161
8.
Time:9:00-10:00, Wednesday, December 6
Speaker:Gong Chen, Georgia Institute of Technology
Title:Dynamics of multi-solitons to Klein-Gordon equations
Abstract:I will report my recent joint work with Jacek Jendrej on muti-solitons to the Klein-Gordon equations including their asymptotic stability and classification.
ZOOM ID：845 4004 6143
Password：758650
9.
Time:14:00-15:00, Wednesday, December 14
Speaker:Ilyas Khan, University of Oxford
Title:Uniqueness of Asymptotically Conical Gradient Shrinking Solitons in G_2-Laplacian Flow
Abstract:In this talk, we will discuss recent joint work with M. Haskins and A. Payne in which we prove the uniqueness of asymptotically conical gradient shrinking solitons of Bryant's Laplacian flow for closed G_2 structures. We will particularly emphasize the unique difficulties that arise in the setting of Laplacian flow (in contrast to the Ricci flow, where an analogous result due to Kotschwar and Wang is well-known) and how to overcome these difficulties.
ZOOM ID：952 5507 2049
Password：789257
10.
Time:14:00-15:00, Wednesday, December 21
Speaker:Yuto Yamamoto, IBS Center for Geometry and Physics
Title:Tropical varieties and integral affine manifolds with singularities
Abstract:There are two types of spaces which we study in tropical geometry. One is tropical varieties which appear as the tropicalizations of algebraic varieties over a valuation field. The other one is integral affine manifolds with singularities which arise as the dual intersection complexes of toric degenerations in the Gross--Siebert program. In the talk, we discuss relations between these two different types of tropical spaces. We construct contraction maps from tropical Calabi--Yau varieties to corresponding integral affine manifolds with singularities, and show that they preserve tropical (co)homology groups and the invariants of tropical structures called eigenwaves/radiance obstructions.
ZOOM ID：922 4936 6933
Password：068397
11.
Time:10:30-11:30, Wednesday, December 22
Speaker:Kartick Ghosh, Indian Institute of Science
Title:Coupled K\"ahler-Einstein and Hermitian-Yang-Mills equations
Abstract:We shall discuss coupled K\"ahler-Einstein and Hermitian-Yang-Mills equations. First, we shall provide a moment map interpretation of these equations. We then give some nontrivial examples of solutions. The first example uses deformation. The other examples are on some projective bundles and use the famous Calabi ansatz. We shall also talk about a Futaki-type invariant which is an obstruction to the existence of solutions of the coupled equations.
ZOOM ID：999 1878 6499
Password：468873
12.
Time:14:00-15:00, Wednesday, December 28
Speaker:Minghao Miao, Nanjing University
Title:Kahler-Ricci Flow on Fano threefolds
Abstract:Fano manifolds are important geometric objects in algebraic geometry, which have positive curvature. It is known that they have been classified in 1,10 and 105 families in dimensions 1,2 and 3 respectively. An important question is to study the existence of canonical metric on them, and Kahler-Ricci flow provides a way to describe them. In this talk, I will focus on one family of Fano threefolds, which is obtained by blowing up the smooth quadric threefold along an elliptic curve. I will discuss that this family provide a new examples of Fano manifolds of the lowest dimension on which Kahler-Ricci flow develops type II singularity. This is a joint work with Gang Tian.
ZOOM ID：859 6776 4484
Password：815143
