Upcoming talk:
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.
Past talks:
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.
