Difference between revisions of "Geometry and Topology Seminar"
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Revision as of 12:10, 29 September 2021
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.
|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|
|Oct. 22||Chenxi Wu|
|Oct. 29||Brian Hepler|
|Nov. 5||Botong Wang|
|Nov. 12||Sigurd Angenent|
I'll describe some history, recent results, and open problems about harmonic map flow, particularly in the 2-dimensional case.
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.
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.
I will overview old and new results which show how the presence of singularities affects the topology of complex projective hypersurfaces.
Archive of past Geometry seminars