Geometry Seminar
Fall 2020
Thursdays (and sometimes Tuesdays) 3:404:30pm, in
Ryerson 358 (currently on zoom)

 Thursday October 01 at 2:303:30pm in Zoom
 Danny Calegari, University of Chicago
 Torelli, Johnson, Complete Intersections

Abstract: This is an expository preseminar touching
on two separate topics: mapping class groups and the Johnson
homomorphism; and complete intersections and their
(co)homology. This preseminar aims to provide a little bit
of background for Matthias Kreck’s regular seminar talk
3:404:30.

 Thursday October 01 at 3:404:30pm in Zoom
 Matthias Kreck, Bonn
 Mapping class group of smooth manifolds which look like complex 3dimensional complete intersections

Abstract: Nonsingular complete intersections of
dimension n in CP^{n+k} are important examples of
smooth manifolds. By the Lefschetz hyperplane theorem, the
cohomology is isomorphic to that of CP^{n} except in
the middle dimension and, for n>1, they are simply
connected. In this talk I will report about recent work with
Su Yang about the mapping class group of complex
3dimensional complete intersections or more generally
smooth 6manifolds which look like those. It turns out that
most of the results look rather similar to the case of
oriented surfaces. What is meant by this and what the
differences are will be explained in the talk.

 Thursday October 08 at 3:404:30pm in Zoom
 Kevin Schreve, University of Chicago
 Coxeter groups, CAT(0) geometry, and Euler characteristics

Abstract: This is an expository talk on the subjects
in the title. We'll talk about the CharneyDavis conjecture,
a combinatorial anologue of Hopf's conjecture on Euler
characteristics of nonpositively curved manifolds, and
Davis's construction of locally CAT(0) manifolds using
Coxeter groups . Then we will hopefully talk about some
other constructions one can do with Coxeter groups.

 Thursday October 15 at 3:404:30pm in Zoom
 Henrik Matthiesen, University of Chicago
 From Berger's isoperimetric problem to new minimal surfaces

Abstract: This will be an expository talk trying to
given an idea of the connection of sharp bounds for
eigenvalue problems on surfaces and minimal surfaces. This
development started from Nadirashvili's solution of Berger's
isoperimetric problem 25 years ago, which in turn relied in
part on the by now classical MontielRos paper from 10
years earlier. The problem asks to identify the unit area
metric on a two dimensional torus for which the first
eigenvalue (among unit area metrics) is the largest.
Nadirashvili's argument uses a surprising connection of this
problem to minimal surfaces in spheres. In recent years this
connection has been used to construct a variety of new
minimal surfaces by solving eigenvalue optimization problems
which I will discuss a bit if time permits.

 Thursday October 29 at 2:403:30pm in Zoom
 Kasia Jankiewicz, University of Chicago
 Kazhdan's Property (T)

Abstract: This is an expository talk providing a bit
of background on Property (T) for Dawid Kielak's seminar
talk at 3:40.

 Thursday October 29 at 3:404:30pm in Zoom
 Dawid Kielak, Oxford
 Automorphisms of free groups and Kazhdan's property (T)

Abstract: I will discuss the proof of the following
theorem: Aut(F_{n}) has property (T) if and only if
n > 3. This is joint work with M. Kaluba and P. Nowak,
though we will need results of KalubaNowakOzawa and
Nitsche

 Thursday November 05 at 3:404:30pm in Zoom
 Andre Neves, University of Chicago
 Positive Scalar Curvature I

Abstract: I will survey the problem of which
manifolds admit metrics of positive scalar curvature and
explain why the answer is known for 3manifolds.

 Thursday November 12 at 2:403:30pm in Zoom
 Andre Neves, University of Chicago
 Positive Scalar Curvature II

Abstract: I will explain what is a Gromov \mu bubble
and how that helps in showing that no aspherical 4manifold
has a metric of positive scalar curvature.

 Thursday November 12 at 3:404:30pm in Zoom
 Chao Li, Princeton University
 Generalized soap bubbles and the topology of manifolds with positive scalar curvature

Abstract: It has been a classical question which
manifolds admit Riemannian metrics with positive scalar
curvature. I will present some recent progress on this
question, ruling out positive scalar curvature on closed
aspherical manifolds of dimensions 4 and 5 (as conjectured
by SchoenYau and by Gromov), as well as complete metrics of
positive scalar curvature on an arbitrary manifold connect
sum with a torus. Applications include a SchoenYau
Liouville theorem for all locally conformally flat
manifolds. The proofs of these results are based on
analyzing generalized soap bubbles  surfaces that are
stable solutions to the prescribed mean curvature problem.
This talk is based on joint work with O. Chodosh.
Due to the high number of requests, we are no longer accepting speakers via selfinvitations.
For questions, contact