Geometric Analysis

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Geometric Analysis

 May 28 - Jun 01, 2018
 ICMS, 15 South College Street Edinburgh

Scientific Organisers:

  • Mihalis Dafermos, University of Cambridge

  • Andre Neves, Imperial College London

  • Peter Topping, University of Warwick

 

Geometric analysis represents one of the most active and exciting areas of mathematics. It lies at the intersection of differential geometry, analysis, partial differential equations and mathematical physics, and is having a profound impact on all these fields, leading to the resolution of many conjectures as well as stimulating important new avenues of research.

The workshop focused on three of the most active subareas, namely geometric flows, variational methods and mathematical relativity. It also covered manifolds with controlled Ricci tensor, which has seen spectacular progress over the past few years and is currently accumulating many promising links with geometric flows and a wide array of applications. This workshop brought together this field's leading researchers leaders in the field and provided first-hand access to the most current research for students. A selection of photographs of the workshop group is available here.

 

Speakers:

  • Richard Schoen, University of California - The Positive Mass Theorem Revisited

  • Jonathan Luk, Stanford University - Strong Cosmic Censorship in General Relativity

  • Sergiu Klainerman, Princeton University - On the Non-Linear Stability of Black Holes

  • Gerhard Huisken, Tubingen University - Inverse Mean Curvature Flow of Entire Graphs

  • Lu Wang, University of Wisconsin - Asymptotic Structure of Self-Shrinkers of Mean Curvature Flow

  • Esther Cabezas-Rivas, Goethe-Universität Frankfurt - Brownian Motion on Perelman's Almost Ricci-Flat Manifold

  • Daniele Valtorta, University of Zurich - Energy Identity for Stationary Yang Mills Connections

  • Manuel Del Pino, University of Bath - Vortex Dynamics in Euler Flows and the Liouville Equation

  • Neshan Wickramasekera, University of Cambridge - Regularity of Minimal and CMC Stable Hypersurfaces

  • Christos Mantoulidis, MIT - Allen--Cahn Min-Max in 3-Manifolds

  • Song Sun, University of California - Collapsing of HyperKahler Metrics on K3 surfaces

  • Reto Buzano, Queen Mary University London - Geometric Convergence Results for Closed Minimal Surfaces via Bubbling Analysis

  • Maria Colombo, ETH Zurich - Direct Epiperimetric Inequalities for the Classical and Thin Obstacle Problem

  • Tristan Riviere, ETH Zurich - Min-Max Minimal Surfaces in Arbitrary Co-Dimensions and the Multiplicity One Conjecture

  • Ailana Fraser, University of British Columbia - Shape Optimisation for an Eigenvalue Problem on Manifolds with Boundary

  • Henrik Matthiesen, MPIM Bonn - The Systole of Large Genus Minimal Surfaces in Positive Ricci Curvature

  • Antoine Song, Princeton University - Equine-Distribution of Minimal Hypersurfaces for Generic Metrics

  • Otis Chodosh, Princeton University - Allen--Cahn Min-Max in 3-Manifolds

  • Dan Ketover, Princeton University - On the Existence of Minimal Surfaces Isotopic to a Heegaard Surface

 
This workshop is jointly funded by ICMS and the Singularities of Geometric Partial Differential Equations EPSRC programme grant.