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Deformation of spherical conical metrics

Recent developments in microlocal analysis October 14, 2019 - October 18, 2019

October 14, 2019 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Xuwen Zhu (University of California, Berkeley)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Spherical conical metrics

  • deformation

  • uniformization

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
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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 and Bin Xu.

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