Upcoming talk:
Date&Time: June. 27th, 2025, 14:00-15:00
Venue: Jingzhai (静斋) 218
Speaker: Zetian Yan (UC Santa Barbara)
Title: Recent progress on fourth order Willmore energy
Abstract: We introduce a fourth-order Willmore-type problem for closed four-dimensional submanifolds immersed in $R^n$ and establish a connected sum energy reduction for the general fourth-order Willmore energy, analogous to the seminal result of Bauer and Kuwert. We will also discuss recent progress on the study of energy quantization on fourth order Willmore energy.
Past talks:
Date&Time: May. 27th, 2025, 13:30-14:30
Venue: 双清C654
Title: Mass Lower Bounds for asymptotically locally flat 4-manifolds
Speaker:Jian Wang (王健) （中国科学院数学研究所）
Abstract: The mass, a crucial global geometric invariant, intricately relates with
scalar curvature in the different setting. I will explain the relation between asymptotically locally flat (ALF) 4-manifolds and their ADM mass. Specifically, I will talk about how the topology at infinity influences the ADM mass within the ALF setting.
Date&Time: Mar. 12th, 2025, 10:00-11:00 am (Beijing time)
Venue: online zoom meeting: 890 9835 3295 Password: 111111
Speaker: Omar Alshawa (University of Toronto)
Title: Riemannian 3-spheres that are hard to sweep out by short curves
Abstract:
Does every Riemannian 3-sphere M contain a closed geodesic whose length is bounded from above by some function f(d,V) of the diameter d and volume V of M? One strategy to find such a closed geodesic is to construct a sweepout of M by closed curves of length at most f(d,V). In collaboration with Herng Yi Cheng, we prove that this method of finding short closed geodesics does not work for a certain class of sweepouts.
Let L>0 be large. We show that there exists M of diameter and volume less than 1 such that for any sweepout of M by closed curves within this class, one of the curves must be longer than 1.
Date&Time: Jan. 2nd, 2025, 14:00-15:00
Venue: 线上腾讯会议：832-674-246 Password: 111111
Speaker: Jintian Zhu (朱锦天) (Westlake University)
Title: Splitting theorem for Kähler manifolds
Abstract: In this talk, we will establish a Cheeger-Gromoll type splitting theorem for Kähler manifolds with nonnegative mixed curvature based on the conformal method. For our purpose, first we will recall basic knowledge on the Cheeger-Gromoll splitting theorem and Kähler manifolds, and then we will present our theorem and its proof with the conformal method in detail.
Date&Time: Nov. 27, 2024, 10:30-11:30 am
Venue: Online Zoom Meeting ID: 834 6034 2049 Password: 111111
Speaker: Yujie Wu (Stanford University)
Title: The $\mu$-bubble Construction of Capillary Surfaces
Abstract: We introduce a method of constructing (generalized) capillary surfaces via Gromov's "$\mu$-bubble" method. Using this, we study low-dimensional manifolds with nonnegative scalar curvature and strictly mean convex boundary. We prove a fill-in question of Gromov, a band-width estimate, and a compactness conjecture of Martin. Li in the case of surfaces.
Introduction: Yujie Wu is currently a Ph.D. Student at Stanford University advised by Prof. Otis Chodosh. Her research focused on geometric analysis and PDEs, in particular minimal surface theory and the Allen Cahn equation.
