Arizona State University

Tue 27 Mar 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

A uniqueness theorem for asymptotically cylindrical shrinking Ricci solitons

ESB 2012
Tue 27 Mar 2018, 3:30pm4:30pm
Abstract
I will discuss some recent joint work with Lu Wang in which we prove that a shrinking gradient Ricci soliton which agrees to infinite order at spatial infinity with a generalized cylinder along some end must be isometric to the cylinder on that end. When the shrinker is complete, it must be globally isometric to the cylinder or else to a Z_2quotient. This work belongs to a larger program aimed at obtaining a structural classification of complete noncompact shrinking solitons.
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Eberhard Karls University, Tuebingen

Tue 3 Apr 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

TBA

ESB 2012
Tue 3 Apr 2018, 3:30pm4:30pm
Abstract
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Stanford University

Tue 10 Apr 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

TBA

ESB 2012
Tue 10 Apr 2018, 3:30pm4:30pm
Abstract
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University of Toronto

Tue 17 Apr 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Geometric Inequalities on Riemannian manifolds

ESB 2012
Tue 17 Apr 2018, 3:30pm4:30pm
Abstract
I will discuss some upper bounds for the length of a shortest periodic geodesic, and the smallest area of a closed minimal surface on closed Riemannian manifolds of dimension 4 with Ricci curvature between 1 and 1. These are the first bounds that use information about the Ricci curvature rather than sectional curvature of the manifold. (Joint with Nan Wu).
I will also give examples of Riemannian metrics on the 3disk demonstrating that the maximal area of 2spheres arising during an ``optimal" homotopy contracting its boundary cannot be majorized in terms of the volume and diameter of the 3disc and the area of its boundary. This contrasts with earlier 2dimensional results of Y. Liokomovich, A. Nabutovsky and R. Rotman and answers a question of P. Papasoglu. On the other hand I will show that such an upper bound exists if, instead of the volume, one is allowed to use the first homological filing function of the 3disc. (Joint with Parker GlynnAdey).
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