Geometry Seminar
Winter 2021
Thursdays (and sometimes Tuesdays) 3:404:30pm, in
Ryerson 358 (currently on zoom)

 Thursday January 21 at 3:404:30pm in Zoom
 Kevin Schreve, University of Chicago
 Invariant random subgroups

Abstract: This talk is intended to provide some
background for Mikolaj Fraczyk's talk next week. I will
introduce the Chabauty topology, BenjaminiSchramm
convergence, and invariant random subgroups.

 Thursday January 28 at 3:404:30pm in Zoom
 Mikolaj Fraczyk, University of Chicago
 Injectivity radius of discrete subgroups of higher rank groups

Abstract: Let G be a simple higher rank Lie group
and let X be the associated symmetric space. Margulis
conjectured that any discrete subgroup Gamma of G such that
X/Gamma has uniformly bounded injectivity radius must be a
lattice. I will present the proof of this conjecture and
explain how stationary random subgroups play the central
role in the argument. The talk will be based on a recent
joint work with Tsachik Gelander.

 Thursday February 4 at 3:404:30pm in Zoom
 Alexander Olshanskiy, Vanderbilt University and Moscow State University
 Geometry of relations in torsion groups and monsters. Part I

Abstract: Tarski monsters are groups with unusual
properties. For instance, there are infinite simple groups,
where every proper subgroup is finite cyclic. Such groups
were constructed about 40 years ago. They became
counterexamples to many known problems. Kasia Jankiewicz
has asked the speaker to give a talk related to monsters.
The task turned out to be not easy since (a) the
constructions are not short and (b) the papers were
published long time ago. The talk will be subdivided in two
parts. In the first part (Feb. 4), I want to explain how van
Kampen diagrams work in the classical Small Cancellation
Theory. (This is for the participant who are not familiar
with small cancellations; everything will be defined and
proved.) In the second part (Feb. 11), I am going to
introduce more specific diagrams, which help to construct
various torsion groups and monsters.

 Thursday February 11 at 3:404:30pm in Zoom
 Alexander Olshanskiy, Vanderbilt University and Moscow State University
 Geometry of relations in torsion groups and monsters. Part II

Abstract: Tarski monsters are groups with unusual
properties. For instance, there are infinite simple groups,
where every proper subgroup is finite cyclic. Such groups
were constructed about 40 years ago. They became
counterexamples to many known problems. Kasia Jankiewicz
has asked the speaker to give a talk related to monsters.
The task turned out to be not easy since (a) the
constructions are not short and (b) the papers were
published long time ago. The talk will be subdivided in two
parts. In the first part (Feb. 4), I want to explain how van
Kampen diagrams work in the classical Small Cancellation
Theory. (This is for the participant who are not familiar
with small cancellations; everything will be defined and
proved.) In the second part (Feb. 11), I am going to
introduce more specific diagrams, which help to construct
various torsion groups and monsters.

 Thursday February 18 at 3:404:30pm in Zoom
 Danny Calegari, University of Chicago
 Preliminary talk for Daniil's talk

Abstract: This is an expository talk. We will give a
gentle introduction to volumes of hyperbolic polyhedra,
focusing mainly on dimensions 2 and 3. We discuss the
Schlafli formula, the dilogarithm, and perhaps say a few
words about orthoschemes and their parameterization.

 Thursday February 25 at 3:404:30pm in Zoom
 Daniil Rudenko, University of Chicago
 Goncharov depth conjecture and volumes of hyperbolic orthoschemes

Abstract: The talk will be about an explicit formula
for volumes of hyperbolic orthoschemes, which generalises
the formula of Lobachevsky to an arbitrary dimension. Quite
unexpectedly, a slight modification this formula can be used
to prove a conjecture of Goncharov on depth of multiple
polylogarithms.

 Thursday March 4 at 3:404:30pm in Zoom
 Clara Löh, Universität Regensburg
 The spectrum of simplicial volume: Foundations.

Abstract: This is the first talk in a series of two.
Simplicial volume is a homotopy invariant of closed
manifolds that is related to Riemannian geometry. We review
the basics and how one can pass from group homology to
simplicial volumes of manifolds.

 Thursday March 11 at 3:404:30pm in Zoom
 Nicolaus Heuer, Tudor Investment Corporation
 The spectrum of simplicial volume: Using scl.

Abstract: This is the second talk in a series of
two. We explain how stable commutator length can be used to
show that the set of simplicial volumes of closed
4manifolds has no gap at 0 and that arbitrarily small
transcendental values occur.
Due to the high number of requests, we are no longer accepting speakers via selfinvitations.
For questions, contact