Student Geometric Analysis Seminar, Fall 2018

Below is a calendar of upcoming talks in the Columbia Student Geometric Analysis Seminar. Titles will typically be posted the weekend before the talk.

Time and location: Monday 16:30-18:00 in Math 520.

Date Speaker Title Ref. / Abstract
17 Sep Keaton Naff Hamilton's Maximum Principle Chow and Lu (2004)
24 Sep Beomjun Choi Convex Inverse Mean Curvature Flow with Singularities and its Smoothing Time Using local speed estimate of the inverse mean curvature flow recently shown by B. Choi and P. Daskalopoulos, we investigate the singularity evolution of IMCF under convexity assumption. The exact smoothing time will be obtained as a corollary. This is joint work with Pei-Ken Hung.
1 Oct Freid Tong Gromov Hausdorff Limits of Algebraic Manifolds Donaldson-Sun (2014)
8 Oct Freid Tong Gromov Hausdorff Limits of Algebraic Manifolds (2) Donaldson-Sun (2014)
15 Oct Semon Rezchikov Gluing theory for CY metrics on K3s Donaldson (2010)
22 Oct Aaron Chow Self-Expanders to Inverse Curvature Flow by Homogeneous Functions We study self-expanding solutions to a large class of parabolic inverse curvature flows by homogeneous symmetric functions of principal curvatures in Euclidean spaces. These flows include the inverse mean curvature flow and many nonlinear flows in the literature. We show that the only compact self-expanders to any of these flows are round spheres.
29 Oct Jingze Zhu Nash-Moser Harnack Inequality for Parabolic Equations
5 Nov No Meeting Election Day
12 Nov Beomjun Choi Evolution of Non-Compact Hypersurface By Inverse Mean Curvature In this talk, we give an existence theorem of the inverse mean curvature flow for an arbitrary convex non-compact hypersurfaces in Euclidean space. The key ingredient of the proof is an a priori estimate of the weighted speed $(H|F|)^{-1}$ which does not depend on its initial bound. The maximal time of existence is explicitly given by the area of initial cone and the solution becomes flat as time approaches to it. This is a joint work with P. Daskalopoulos.
19 Nov Keaton Naff Bounded Ricci Tensor in Ricci Flow Sesum (2005)
26 Nov No Meeting Thanksgiving
3 Dec Kevin Smith C^0 Estimate for Hermitian Manifolds Tosatti & Weinkove (2009)