Geometry/Topology Seminar
Spring 2019
Thursdays (and sometimes Tuesdays) 2:303:30pm, in
Ryerson 358

 Thursday April 4 at 2:303:30pm in Ry 358
 Weiyan Chen, Minnesota
 Cohomology of the space of complex irreducible polynomials in
several variables

Abstract: We will show that the space of complex
irreducible polynomials of degree d in n variables satisfies
two forms of homological stability: first, its cohomology
stabilizes as d increases, and second, its compactly
supported cohomology stabilizes as n increases. Our
topological results are inspired by counting results over
finite fields due to Carlitz and Hyde.

 Friday April 12 at 45pm in Ry 251
 Vladimir Markovic, California Institute of Technology
 Namboodiri Lecture 1: The Surface Subgroup Problem

Abstract: The surface subgroup problem asks whether
a given group contains a subgroup that is isomorphic to the
fundamental group of a closed surface. In this talk I will
survey the role the surface subgroup problem plays in some
important solved and unsolved problems in 3manifold
topology, the theory of arithmetic manifolds and geometric
group theory.

 Monday April 15 at 45pm in Ry 251
 Vladimir Markovic, California Institute of Technology
 Namboodiri Lecture 2: Rigidity and geometry of Harmonic Maps

Abstract: Harmonic maps play a prominent role in
geometry. I will explain some of these applications
including Siu's rigidity of negatively curved Kahler
manifolds and the CorletteGromovSchoen rigidity of
representations theorem, as well as the very recent results
of Markovic and BenoistHulin about the existence and
uniqueness of harmonic maps between rank1 symmetric spaces.

 Tuesday April 16 at 45pm in E 206
 Vladimir Markovic, California Institute of Technology
 Namboodiri Lecture 3: Teichmueller flow and complex geometry of Moduli Spaces

Abstract: I will explain why in general the
Caratheodory and Teichmueller metrics do not agree on
Teichmueller spaces and why this yields a proof of the
convexity conjecture of Siu. Moreover, I will illustrate how
deep theorems in Teichmueller dynamics play an important
role in classifying Teichmueller discs where the two metrics
agree.

 Thursday April 18 at 2:303:30pm in Ry 358
 Sam Nariman, Northwestern
 Dynamical and cohomological obstruction to extending group actions

Abstract: For any 3manifold M with torus
boundary, we find finitely generated subgroups of
\Diff_{0}(\partial M) whose actions do
not extend to actions on M; in many cases, there
is even no action by homeomorphisms. The obstructions are
both dynamical and cohomological in nature. We also show
that, if \partial M = S^{2}, there is no
section of the map \Diff_{0}(M) \to
\Diff_{0}(\partial M). This is joint work with
Kathryn Mann.

 Friday April 26 at 3:304:30pm in Eck 306
 Jenny Wilson, Michigan
 Representation Stability

Abstract: This talk will give an overview of the
recent field of 'representation stability'. I will discuss
how we can use representation theory to illuminate the
structure of certain families of groups and topological
spaces with actions of the symmetric groups S_{n},
focusing on configuration spaces as an illustrative example.

 Thursday May 9 at 2:303:30pm in Ry 358
 Alex Duncan, South Carolina
 Finite Subgroups of Cremona Groups

Abstract: The Cremona group of rank n is the group
of birational automorphisms of ndimensional projective
space. While the group of regular automorphisms of
projective space is just the projective general linear
group, the presence of denominators means that Cremona
groups are far larger for rank 2 and beyond. However, using
ideas from the minimal model program, one can study its
finite subgroups by considering honest regular automorphisms
of related spaces. I will overview what is known about
Cremona groups from this perspective.

 Thursday May 16 at 2:303:30pm in Ry 358
 Kathryn Mann, Brown
 Structure theorems for actions of homeomorphism groups

Abstract: The groups Homeo(M) and Diff(M) of
homeomorphisms or diffeomorphisms of a manifold M have many
striking parallels with finite dimensional Lie groups. In
this talk, I'll describe some of these, explaining new joint
work with Lei Chen. We give an orbit classification theorem
and a structure theorem for actions of homeomorphism and
diffeomorphism groups on other spaces, analogous to some
classical results for actions of locally compact Lie groups.
As applications, we answer many concrete questions towards
classifying all actions of Diff(M) on other manifolds (many
of which are nontrivial, for instance Diff(M) acts naturally
on the unit tangent bundle of M...) and resolve several
threads in a research program initiated by Ghys.

 Tuesday May 28 at 2:303:30pm in Ry 358
 Corey Bregman, Brandeis
 Kodaira Fibrations with Invariant Cohomology

Abstract: A Kodaira fibration is a complex surface
admitting a holomorphic submersion onto a curve, whose
fibers have nonconstant moduli. Kodaira and Atiyah
independently constructed the first examples of Kodaira
fibrations, by taking a branched cover of a product of
curves. Conversely, we show that when a Kodaira fibration
has nontrivial holomorphic invariants of dimension at most
two, it admits a branched covering over a product of curves.
Due to the high number of requests, we are no longer accepting speakers via selfinvitations.
For questions, contact