Geometry and Topology Seminar

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The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1pm - 2:20pm. For more information, contact Alex Waldron.


Fall 2021

date speaker title
Sep. 10 Organizational meeting
Sep. 17 Alex Waldron Harmonic map flow for almost-holomorphic maps
Sep. 24 Sean Paul Geometric Invariant Theory, Stable Pairs, Canonical Kähler metrics & Heights
Oct. 1 Andrew Zimmer Entropy rigidity old and new
Oct. 8 Laurentiu Maxim Topology of complex projective hypersurfaces
Oct. 15 Gavin Ball Introduction to G2 Geometry
Oct. 22 Chenxi Wu
Oct. 29 Brian Hepler
Nov. 5 Botong Wang
Nov. 12 Sigurd Angenent

Fall Abstracts

Alex Waldron

I'll describe some history, recent results, and open problems about harmonic map flow, particularly in the 2-dimensional case.

Sean Paul

An interesting problem in complex differential geometry seeks to characterize the existence of a constant scalar curvature metric on a Hodge manifold in terms of the algebraic geometry of the underlying variety. The speaker has recently solved this problem for varieties with finite automorphism group. The talk aims to explain why the problem is interesting (and quite rich) and to describe in non-technical language the ideas in the title and how they all fit together.

Note: this talk will provide some background for Sean's colloquium later in the afternoon.

Andrew Zimmer

Informally, an "entropy rigidity" result characterizes some special geometric object (e.g. a constant curvature metric on a manifold) as a maximizer/minimizer of some function of the objects asymptotic complexity. In this talk I will survey some classical entropy rigidity results in hyperbolic and Riemannian geometry. Then, if time allows, I will discuss some recent joint work with Canary and Zhang. The talk should be accessible to first year graduate students.

Laurentiu Maxim

I will overview old and new results which show how the presence of singularities affects the topology of complex projective hypersurfaces.

Gavin Ball

I will give an introduction to the theory of manifolds with holonomy group G2. I will begin by describing the exceptional Lie group G2 using some special linear algebra in dimension 7. Then I will give an overview of the holonomy group of a Riemannian manifold and describe Berger's classification theorem. The group G2 is one of two exceptional members of Berger's list, and I will explain the interesting properties manifolds with holonomy G2 have and sketch the construction of examples. If time permits, I will describe some of my recent work on manifolds with closed G2-structure.

Archive of past Geometry seminars

2020-2021 Geometry_and_Topology_Seminar_2020-2021

2019-2020 Geometry_and_Topology_Seminar_2019-2020

2018-2019 Geometry_and_Topology_Seminar_2018-2019

2017-2018 Geometry_and_Topology_Seminar_2017-2018

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