Geometry and Topology Seminar 2019-2020

The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
For more information, contact Alexandra Kjuchukova or Lu Wang .

Fall 2017

date	speaker	title	host(s)
September 8	TBA	TBA	TBA
September 15	Jiyuan Han (University of Wisconsin-Madison)	"On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"	Local
September 22	Sigurd Angenent (UW-Madison)	"Topology of closed geodesics on surfaces and curve shortening"	Local
September 29	Ke Zhu (Minnesota State University)	"Isometric Embedding via Heat Kernel"	Bing Wang
October 6	Shaosai Huang (Stony Brook)	"\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"	Bing Wang
October 13	Sebastian Baader (Bern)	TBA	Kjuchukova
October 20	Shengwen Wang (Johns Hopkins)	TBA	Lu Wang
October 27	Marco Mendez-Guaraco (Chicago)	TBA	Lu Wang
November 3	TBA	TBA	TBA
November 10	TBA	TBA	TBA
November 17	Ovidiu Munteanu (University of Connecticut)	TBA	Bing Wang
Thanksgiving Recess
December 1	TBA	TBA	TBA
December 8	Brian Hepler (Northeastern University)	TBA	Max

Fall Abstracts

Jiyuan Han

"On closeness of ALE SFK metrics on minimal ALE Kahler surfaces"

Under some topological assumption (which gives the boundedness of Sobolev constant), we construct the space of ALE SFK metrics on minimal ALE Kahler surfaces asymptotic to C^2/G, where G is a finite subgroup of U(2). This is a joint work with Jeff Viaclovsky.

Sigurd Angenent

"Topology of closed geodesics on surfaces and curve shortening"

A closed geodesic on a surface with a Riemannian metric defines a knot in the unit tangent bundle of that surface. Which knots can occur? Given a particular knot type, what is the lowest number of closed geodesics a surface must have if you are allowed to pick the metric on the surface? Curve shortening allows you to define an invariant for each knot type (called the Conley index) which gives some answers to these questions.

Ke Zhu

"Isometric Embedding via Heat Kernel"

The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding. In this talk, using the eigenfunctions of the Laplacian operator, we construct canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces, and study the geometry of embedded images. They turn out to have large mean curvature (intuitively, very bumpy), but the extent of oscillation is about the same at every point. This is a joint work with Xiaowei Wang.

Shaosai Huang

"\epsilon-Regularity for 4-dimensional shrinking Ricci solitons"

A central issue in studying uniform behaviors of Riemannian manifolds is to obtain uniform local L^{\infty}-bounds of the curvature tensor. For manifolds whose Riemannian metric satisfying certain elliptic equations, e.g. Einstein manifolds and Ricci solitons, local curvature bound are expected when the local energy is sufficiently small. Such estimates, referred to as \epsilon-regularity, are usually obtained via Moser iteration arguments, which requires a uniform control of the Sobolev constant. This requirement may fail in many natural situations. In this talk, I will discuss an \epsilon-regularity result for 4-dimensional shrinking Ricci solitons without a priori control of the Sobolev constant.

Shengwen Wang

"TBA"

Marco Mendez-Guaraco

"TBA"

Ovidiu Munteanu

"TBA"

Archive of past Geometry seminars

2016-2017 Geometry_and_Topology_Seminar_2016-2017

2015-2016: Geometry_and_Topology_Seminar_2015-2016

2014-2015: Geometry_and_Topology_Seminar_2014-2015

2013-2014: Geometry_and_Topology_Seminar_2013-2014

2012-2013: Geometry_and_Topology_Seminar_2012-2013

2011-2012: Geometry_and_Topology_Seminar_2011-2012

2010: Fall-2010-Geometry-Topology