Constant curvature conical metrics

Abstract: The problem of finding and classifying constant curvature metrics with conical singularities has a long history bringing together several different areas of mathematics. This talk will focus on the particularly difficult spherical case where many new phenomena appear. When some of the cone angles are bigger than $2\pi$, 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, connecting microlocal techniques with complex analysis and synthetic geometry. Based on joint works with Rafe Mazzeo, Bin Xu, and Mikhail Karpukhin.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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The livestream is on Zoom at : uqam.zoom.us/j/98999725241 (no password is needed).

The recorded talks can be found at CIRGET channel : www.youtube.com/channel/UCLkFm-uEvXSf9y-iQtWOLWA