## Activities

1. YMSC Courses Mini Courses Seminars Lectures Conferences

## Differential Geometry seminar

Organizer：杨晓奎，张蓥莹
Time：
Venue：

# Upcoming Talks

Speaker：Teng Fei (Rutgers University – Newark)

Title: Symplectic deformations and the Type IIA flow

Time: Monday,10:30-11:30am, August 15, 2022

Venue: Online Tencent ID: 989-836-015; Offline: Lecture Hall, Jinchun Yuan West Building (近春园西楼三楼报告厅)

Abstract: The equations of flux compactification of Type IIA superstrings were written down by Tomasiello and Tseng-Yau. To study these equations, we introduce a natural geometric flow known as the Type IIA flow on symplectic Calabi-Yau 6-manifolds. We prove the wellposedness of this flow and establish the basic estimates. We show that the Type IIA flow can be applied to find optimal almost complex structures on certain symplectic manifolds. We prove the dynamical stability of the Type IIA flow, which leads to a proof of stability of Kahler property for Calabi-Yau 3-folds under symplectic deformations. This is based on joint work with Phong, Picard and Zhang.

Bio: Teng Fei obtained his Ph.D. from MIT in 2016, under the supervision of Prof. Shing -Tung Yau and Prof. Victor Guillemin. He is currently an assistant professor in the Department of Math & CS of Rutgers University - Newark.

# Past Talks

Speaker: Nicholas McCleerey （University of Michigan）

Title: Lelong Numbers of $m$-Subharmonic Functions Along Submanifolds

Abstract: We study the possible singularities of an $m$-subharmonic function $\varphi$ along a complex submanifold $V$ of a compact K\"ahler manifold, finding a maximal rate of growth for $\varphi$ which depends only on $m$ and $k$, the codimension of $V$. When $k < m$, we show that $\varphi$ has at worst log poles along $V$, and that the strength of these poles is moveover constant along $V$. This can be thought of as an analogue of Siu's theorem. This is joint work with Jianchun Chu.

Time: 04/14/2022, Thu, 9:00-10:00 (Beijing Time)

Location: Online (Zoom)

Meeting ID: 4552601552

Passcode: YMSC

Speaker: 邓富声 （中国科学院大学）

Title:  Analytic characterization of convexity and pseudoconvexity of bounded domains.

Abstract: We show that a bounded domain with smooth boundary is convex (or pseudoconvex) if and only if the first order d-equation (or $\bar{\partial}$-equation) on it is solvable with certain $L^2$-estimate. This is a joint work with Xujun Zhang.

Time: 04/21/2022, Thu, 9:00-10:00 (Beijing Time)

Location: Online (Zoom)

Meeting ID: 4552601552

Passcode: YMSC

Speaker: Gao Chen (USTC)

Title   : Torelli-type theorems for gravitational instantons
Abstract   : A gravitational instanton is a non-compact complete hyperkähler 4-manifold with bounded L^2 curvature. In this talk, We will discuss Torelli-type theorems for gravitational instantons. This is a joint work with Jeff Viaclovsky and Ruobing Zhang.

Time:    01/05/2022, Wednesday, 16:00-17:00 (Beijing Time)
Location:    Online (Zoom)    Offline:近春园三楼报告厅

Meeting ID: 849 963 1368
Passcode:
YMSC

Speaker:Pak-Yeung Chan (UCSD)

Title:   On a dichotomy of the curvature decay of steady Ricci soliton
Abstract:   Ricci soliton arises naturally in the singularity analysis of the Ricci flow. Steady Ricci soliton is closely related to the Type II limit solution to the Ricci flow. There are two generic curvature decays for complete noncompact steady gradient Ricci soliton, namely linear and exponential decays. It is unclear if these are the only two possible decays. We show that this dichotomy holds for four dimensional complete noncompact non Ricci flat steady gradient Ricci soliton with at least linear curvature decay and proper potential function. A similar dichotomy is also shown in higher dimensions under the additional assumption that the Ricci curvature is nonnegative near infinity. As an application, we prove some classification results on steady soliton with fast curvature decay and obtain a dichotomy on the asymptotic geometry at spatial infinity. This talk is based on a joint work with Bo Zhu.

Time:
12/27/2021, Monday, 9:30-10:30am (Beijing Time)
Location:    Online (Zoom)

Meeting ID: 849 963 1368
Passcode:
YMSC

Speaker: Zuoqin Wang (USTC)

Title: Equivariant spectral invariants under compact Lie group action

Abstract: Given a $G$-invariant elliptic pseudodifferential operator on a compact Riemannian $G$-manifold $M$, we study its equivariant spectral invariants. I will explain the role of symplectic geometry in studying the $G$-equivariant spectrum. In particular, I will show how to apply symplectic techniques to study equivariant inverse spectral problems for $G$-invariant Schrodinger operators, the main tool being a generalized Legendre transform in the abelian case, and a generalized Legendre relation in the nonabelian case. This is based on joint works with V. Guillemin (MIT)

Time: 12/16/2021, Thursday, 10:00-11:00am (Beijing Time)

Location: Online (Tencent)

Meeting ID: 531-442-663

Speaker: Fei Han  (National University of Singapore)

Title: Brief Introduction to Genera and Applications

Abstract: The cobordism invariants, genera, play fundamental roles in manifold topology. Some specific genera, like A-hat genus, L-genus, Witten genus and elliptic genus are the topological pillars of the Atiyah-Singer index theory, spin geometry and string geometry. In this minicourse, we will give a brief introduction to genera starting from very basic knowledge and introduce some applications of genera in physics in particular anomaly cancellation problem, and in geometry concerning group actions and curvatures.

Time: 12/04/2021, 19:00-21:00,

12/11/2021, 19:00-21:00

Location: Online (Tecent)

Meeting ID: 607-3894-1091

Speaker: Xin Zhou (Cornell University)

Title: Existence of Constant Mean Curvature surfaces

Abstract: Constant Mean Curvature (CMC) surfaces constitute a classical subject in Differential Geometry and are mathematical models in many disciplines of science. In this talk, I will present some results on the min-max construction of closed CMC surfaces. The talk includes joint works with Da Rong Cheng and Jonathan Zhu.

Time: Dec 7, Tuesday, 10:00-11:00am (Beijing Time)

Location: Online (Zoom)

Meeting ID: 452 695 5035

Speaker: Hengyu Zhou (Chongqing University)

Title: Minimal graphs and related flows in warped product manifolds.

Abstract: In this talk we report our series of results on minimal graphs and related problems in warped product (WP) manifolds. Our motivation is to view WP manifolds as canonical manifolds in the certain sense. Then we introduce our results on minimal graphs, mean curvature flows, inverse mean curvature flows and two types of area minimizing problems in some WP manifolds. This includes of some recent works joint with Gao, Qiang.

Time: Dec 2nd, Thursday, 10:00-11:00am

Location: Online (Tencent meeting)

Meeting ID: 156 932 865

Speaker: Chengjian Yao (Shanghai Tech University)

Title: Einstein-Bogomol’nyi equation and Gravitating Vortex equations on Riemann surfaces、

Abstract: The Einstein’s Fields Equation coupled with an Abelian gauge field and a Higgs field possesses a special type of solution, mathematically known as Einstein-Bogomol’nyi equation and physically known as Cosmic Strings. In this talk, I will present some existence theorems for solutions of such equation and also its close companion Gravitating Vortex equations, introduced from a moment map picture. This is based on the joint work with Garcia-Fernandez and Pingali.

Time: Dec 1st, Wednesday, 15:30-16:30

Location: Online (Tencent meeting)

Meeting ID: 731 188 239

Abstract: 本报告主要讨论产生于微分几何和广义相对论中的几类几何流的分析和几何性质。

Title: The convergence and rigidity of mean curvature flow in arbitrary codimension

Speaker: Prof.  Entao Zhao (Zhejiang University)

Tencent Meeting ID:  168 504 661

Time: 2021-11-06, 14:00-15:00

Abstract: In this talk, I will first review the rigidity and sphere theorems for submanifolds, which are motivations of our research on mean curvature flow. Then I will discuss some convergence results for mean curvature flow of arbitrary codimension. At last, I will talk about our recent results on the rigidity of ancient mean curvature flow under curvature pinching conditions.

This talk is based on the joint works with Prof. Kefeng Liu, Prof. Hongwei Xu and Dr. Li Lei.

Title：Poincare inequality on area-minimizing hypersurfaces

Speaker:  Prof. Qi Ding (Fudan University)

Tencent Meeting ID:   168 504 661

Time:  2021-11-06, 15:30-16:30

Abstract: In this talk, I will talk about Neumann-Poincare inequality on area-minimizing hypersurfaces in Euclidean space and manifolds of almost nonnegative Ricci curvature.