PDE / Analysis Seminar

Tuesday, February 04, 2020 at 4:00pm

Room : 2 - 135, 2-135 182 memorial Drive, MIT Building 2, Cambridge, MA, 02142

Featured Speaker :  Xuwen Zhu (MIT)

Title :  Liouville equations with conical boundary conditions

Abstract

The problem of finding and classifying constant curvature metrics with conical singularities has a long history bringing together several different areas of mathematics. Such metrics corresponds to solutions to a Liouville type equation with conical boundary conditions. This talk will focus on the particularly difficult spherical case where many new phenomena appear. When some of the cone angles are bigger than 2π, uniqueness fails and existence is not guaranteed; smooth deformation is not always possible and the moduli space is expected to have singular strata. I will give a survey of several recent results regarding this singular uniformization problem, where ”resolution of singularities” is the key idea in the analysis, which can be seen as an analogue of the Deligne–Mumford compactification of Riemann moduli spaces. Based on joint works with Rafe Mazzeo and Bin Xu.

Event Type

Conferences/Seminars/Lectures

Events By Interest

Academic

Events By Audience

Public

Events By School

School of Science

Tags

pde_sem, aldixon

Website

http://math.mit.edu/seminars/pde-anal...

Department
Department of Mathematics
Hashtag

#PDEAnalysisSeminar

Contact Email

aldixon@mit.edu

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