Max Dehn Seminar
on Geometry, Topology, Dynamics, and Groups
Spring 2017 Wednesday 3:15  4:15, Room LCB 215
Date  Speaker  Title click for abstract (if available) 
August 31
RTG seminar 
Jenny Wilson
Stanford University 
Representation theory and higherorder stability in the
configuration spaces of a manifold
Let F_k(M) denote the ordered kpoint
configuration space of a connected open manifold M. Work
of Church
and others shows that for a given manifold, as k
increases, this
family of spaces exhibits a phenomenon called homological
"representation stability" with respect to the natural
symmetric
group actions. In this talk I will explain what this
means, and
describe a higherorder "secondary stability" phenomenon
among the
unstable homology classes. The project is work in
progress, joint
with Jeremy Miller.

September 7

Adam Kanigowski
Penn State 
Slow entropy for smooth flows on surfaces
Slow entropy is an useful invariant
when
dealing with systems of
intermediate (polynomial) growth. The most classic
examples are:
horocycle
flows, time changes of nilflows and mixing smooth flows on
surfaces (with
finitely many fixed points). In the talk we will focus
mostly on
computing
slow entropy for the class of smooth flows on twotorus
with one
fixed
point. As a consequence we get that such flows never are
rank one
and that
the order of degeneracy of the fixed point is an
invariant.
Moreover, we
establish variational principle for slow entropy in this
class.

September 19 at 3
JWB 308 *Note unusual time and place* 
Sebastian
Hensel
University of Bonn 
Rigidity and Flexibility for the Handlebody Group
The handlebody group H_g is the
subgroup of
the mapping class group Mod_g of a surface formed by all
those
elements which extend to a given handlebody. In this talk
we will
first show that finite index subgroups of this group are
rigid:
any inclusion into Mod_g is conjugate to the standard
inclusion.
We then discuss flexible behaviour: the existence of
inclusion of
H_g into Mod_h whose image is not conjugate into any
handlebody
subgroup of Mod_h.

October 12

No Seminar: Fall break  
October 19

Daniel Bernazzani
Rice University 
Centralizers in the Group of Interval Exchange
Transformations
In this talk, I will explain why a
typical
interval exchange transformation does not commute with any
other
interval exchanges except for its powers.

November 2

Daniel
Studenmund
University of Utah 
Semiduality from products of trees
A duality group has a pairing
exhibiting
isomorphisms
between its homology and cohomology groups. Many naturally
occurring
groups fail to be duality groups, but are morally very
close. In
this
talk we make this precise with the notion of a semiduality
group
and
show that the lamplighter group is a semiduality group.
We'll
finish
by stating a conjecture for semiduality of arithmetic
groups over
function fields and a positive result for arithmetic
groups acting
on
products of trees. This talk covers work joint with Kevin
Wortman.

November 9

Julien
Paupert
Arizona State University 
Rank 1 deformations of noncocompact hyperbolic lattices
Let X be a negatively curved symmetric space and Gamma a
noncocompact lattice in Isom(X). We show that small,
parabolicpreserving deformations of Gamma into a
negatively
curved symmetric space containing X remain discrete and
faithful.
(The cocompact case is due to Guichard.)
This applies in particular to a version of Johnson and
Millson's
bending deformations, providing for all n infinitely many
noncocompact lattices in SO(n,1) which admit discrete and
faithful
deformations into SU(n,1). We also produce deformations of
the
figure8 knot group into SU(3,1), not of bending type, to
which
the result applies. This is joint work with Sam Ballas and
Pierre
Will.

November 23

No Seminar: Thanksgiving  
December 5 at 3 in LCB 219 *Note unusual time*

Aaron
Brown
University of Chicago 
Zimmer’s conjecture for cocompact lattices
For n at least 3, consider a lattice in Sl(n,R). Zimmer’s
conjecture asserts that every action of the lattice on a
manifold
of dimension at most n2 is finite. Recently, D. Fisher
and S.
Hurtado, and I established Zimmer’s conjecture under the
additional assumption that the lattice is cocompact. I
will give
some background and motivation for the conjecture. I will
outline
our proof and explain a number of tools we use: strong
Propterty
(T), cocycle superrigidity, Ratner’s measure
classification
theorem, and smooth ergodic theory of Z^d actions.

December 7

Martin Deraux
Grenoble 
Nonarithmetic lattices
I will present joint work with Parker
and
Paupert, that allowed us to
exhibit new commensurability classes of nonarithmetic
lattices in
the
isometry group of the complex hyperbolic plane. If time
permits, I
will also explain close ties between our work and the
theory of
discrete reflection groups acting on other 2dimensional
complex
space
forms.

January 18

Gordan Savin
University of Utah 
Affine buildings as sets of lattice functions
Let V be a finite dimensional vector space over a padic field.
The affine building of GL(V) can be constructed as the set of all
lattice
functions on V. Let G be a Chevalley group attached to a simple, split,
Lie algebra over the padic field. I will explain how the affine
building
of G can be constructed as the set of (some) lattice functions on the
Lie
algebra.

January 25

Mladen Bestvina
University of Utah 
Boundary amenability for Out(F_n)
The motivation for the talk is the recent result, joint with Vincent
Guirardel and Camille Horbez, that Out(F_n) admits a topologically
amenable action on a Cantor set. This implies the Novikov conjecture
for Out(F_n) and its subgroups. Most of the talk will be an
introduction to boundary amenability and ways to prove it for simpler
groups.

February 1

Ioannis Konstantoulas
University of Utah 
Discrepancy of general symplectic lattices
The statistics of lattice points in Borel sets have been studied
extensively, both for single lattices like the integral points in
Euclidean space and on average over the space of lattices. The
magnitude of the error term in the approximation is related to
problems in spectral theory and number theory and good error terms
have been obtained for typical lattices using tools from
representation theory. However, averages over closed subspaces over
the space of all lattices are far less accessible and the only
discrepancy results so far have been associated to rank one subgroups
of GL(n). In this work, joint with J. Athreya, we provide power
savings bounds for the number of lattice points of a typical lattice
from the general symplectic ensemble in a nested family of Borel sets.
This is the first example of lattice point statistics for a higher
rank group other than the full GL(n) and SL(n).

February 15

Ken Bromberg
University of Utah 
Univalent maps and renormalized volume
We will discuss some classical results on univalent maps and their
applications to the renormalized volume of hyperbolic 3manifolds. This
is joint work with M. Bridgeman and J. Brock.

February 22

Derrick Wigglesworth
University of Utah 
Distortion and Abelian Subgroups
This talk will focus on abelian subgroups of the mapping class group and
Out(F_n). After relating some structural results, we'll discuss how the
intrinsic Euclidean geometry of abelian subgroups relates to the
geometry of the ambient group.

March 1

Bruce Kleiner
New York University 
Ricci flow, singularities, stability, and the topology of
3manifolds
Ricci flow is a geometric PDE that has had a profound impact on
3dimensional topology. Like many geometric evolution equations, its
solutions develop singularities, and their study has been crucial part
of the story. Soon after introducing Ricci flow in 1982, Hamilton
defined a notion of Ricci flow with surgery, a regularization scheme
that allows one to avoid singularities. Building on many contributions
of Hamilton, in 2003 Perelman used Ricci flow with surgery to prove
Thurston’s Geometrization Conjecture, which includes the 3dimensional
Poincare Conjecture as special case. At the same time, Perelman drew
attention to the ad hoc character of Ricci flow with surgery, and
conjectured the existence of "Ricci flow through singularities”, which
would be a canonical evolution for any Riemannian 3manifold. Recently,
Richard Bamler and I have proven Perelman’s conjecture, and used it to
obtain new information about diffeomorphism groups of 3manifolds.

March 8

Matthew Stover
Temple University 
Proper actions on products of trees
Does a surface group act properly on a finite product of finitevalence
trees? I don't know. I'll discuss two results motivated by this
question, joint with David Fisher, Michael Larsen, and Ralf Spatzier.
One hints toward a positive answer: faithful representations of surface
groups into arithmetic groups in characteristic p. The other result is a
structure theorem for proper actions of CAT(0) groups on products of
trees that hints toward a negative answer; for example, these methods
prove that rightangled Artin groups admitting such proper actions are
products of free and free abelian groups.

March 29

Radhika Gupta
University of Utah 
Intersection form for relative currents and relative outer
space
Using the intersection number between curves, the space of laminations
acts as its own dual space. For free groups, the space of currents acts
as dual to the closure of outer space via the intersection form defined
by Kapovich and Lustig. This intersection form can be used to show that
a fully irreducible outer automorphism acts loxodromically on the free
factor complex. With the goal of understanding reducible outer
automorphism, in this talk I will define relative currents, relative
outer space, discuss the intersection form between them and mention an
application to the relative free factor complex.

April 5

James Farre
University of Utah 
Unbounded geometry in bounded cohomology
We explore the bounded cohomology of closed surface groups whose actions
on hyperbolic 3space may have unbounded geometry. The isometry types
of marked hyperbolic 3manifolds are classified in terms of their end
invariants. We discuss how the classification gives us a criterion for
distinguishing bounded classes in degree 3 for surface groups and, more
generally, finitely generated Kleinian groups without parabolics.

April 12

Bei Wang
University of Utah 
Convergence between Categorical Representations of Reeb
Space and Mapper
The Reeb space, which generalizes the notion of a Reeb graph, is one
of the few tools in topological data analysis and visualization
suitable for the study of multivariate scientific datasets. First
introduced by Edelsbrunner et al., it compresses the components of the
level sets of a multivariate mapping and obtains a summary
representation of their relationships. A related construction called
mapper, and a special case of the mapper construction called the Joint
Contour Net have been shown to be effective in visual analytics.
Mapper and JCN are intuitively regarded as discrete approximations of
the Reeb space, however without formal proofs or approximation
guarantees. An open question has been proposed by Dey et al. as to
whether the mapper construction converges to the Reeb space in the
limit.
In this work, we are interested in developing the theoretical
understanding of the relationship between the Reeb space and its
discrete approximations to support its use in practical data analysis.
Using tools from category theory, we formally prove the convergence
between the Reeb space and mapper in terms of an interleaving distance
between their categorical representations. Given a sequence of refined
discretizations, we prove that these approximations converge to the
Reeb space in the interleaving distance; this also helps to quantify
the approximation quality of the discretization at a fixed resolution.
Joint work with Elizabeth Munch, University at Albany – SUNY Albany.

April 13, 2pm, JWB 333 Note unusual time and place 
Colin Adams
Williams College 
Multicrossing Number of Knots: Turning Knots into Flowers
Knots have traditionally been depicted using projections with crossings
where two stands cross. But what if we allow three strands to cross at a
crossing? Or four strands? Can we find projections of any knot with just
one of these multicrossings? We will discuss these generalizations of
traditional invariants to multicrossing numbers, ubercrossing numbers
and petal numbers and their relation to hyperbolic invariants.

April 19

Leonard Carapezza
University of Utah 
Minimality detection between finite graphs
An infinite sequence in a compact metric space X is called
minimal if it satisfies a weak periodicity condition. A compact metric
space Y is called a minimality detector for X if every non minimal
sequence in X can be taken to a non minimal sequence in Y by a
continuous
function. a priori whether Y is a minimality detector for X depends on
if
we are considering halfinfinite or biinfinite sequences, but I show
this
not to be the case. The question of when one finite graph is a
minimality
detector for another finite graph turns out to be the only interesting
case, and some necessary conditions in this way will be presented.

September 20

Florian
Richter
The Ohio State University 
TBA
TBA

October 18

Marco
Lopez
University of North Texas 
TBA
TBA

October 25

Sanghyun
Kim
Seoul National University 
Free products in Diff(S1)
We prove that if G is a finitely
generated nonvirtuallyabelian
group, then (G X Z) * Z does not embed into Diff^2(S^1). In
particular, the class of subgroups of Diff^r(S^1) is not closed under
taking free products for each r >= 2. We complete the classification
of RAAGs embeddable in Diff^r(S^1) for each integer r, answering a
question in a paper of M. Kapovich. (Joint work with Thomas Koberda)

Archive of past talks Max Dehn mailing list
You may also be interested in the RTG Seminar
Max Dehn Seminar is organized by Mladen Bestvina, Ken Bromberg, Jon Chaika,
Thibaut Dumont Ioannis Konstantoulas, Evelyn Lamb, Donald Robertson, Daniel Studenmund,
Domingo Toledo, and Kevin Wortman.
This web page is maintained by Jon Chaika.