Max Dehn Seminar
on Geometry, Topology, Dynamics, and Groups
Fall 2011
Date  Speaker  Title — click for abstract (if available) 
September 19 
Mladen Bestvina University of Utah 
Factor projections
TBA

September 26 
Ric Wade University of Utah 
Centralizers of Dehn twists on free groups
There is a nice description of the centralizer of a Dehn twist in a
mapping class group given by an exact sequence with the Dehn twist at
one end and the mapping class group a punctured surface at the other end
(you obtain the punctured surface by cutting along the curve associated
to the Dehn twist). We describe a similar picture for Dehn twists in
Out(F_n).

October 3 
Colleen Robles Texas A&M University 
Hodge structures, MumfordTate groups and Schubert varieties
MumfordTate groups are the symmetry groups of Hodge theory.
The study of Hodge structures leads one to consider manifolds (called
MumfordTate domains) that are homogenous with respect to a MumfordTate
group. Schubert varieties are distinguished subvarieties of the
MumfordTate domains. I will describe the relationship between Schubert
varieties and variations of Hodge structure.

November 7 
Nathan Geer Utah State University 
Renormalized TQFTs
In this talk I will discuss some new Topological Quantum Field Theories
(TQFTs) arising from a renormalization of the ReshetikhinTuraev quantum
invariants. I will start by giving an axiomatic definition of the renormalized
quantum invariants. These invariants distinguish manifolds that the usual RT
invariants can not and lead to a generalized Volume Conjecture. I will give
Atiyah's original definition of a TQFT and discuss how the renormalized
invariants lead to such TQFTs. I will finish the talk discussing how these TQFTs
lead to mapping class group representations. These mapping class group
representations have interesting properties including the fact that the action of
certain Dehn twists have infinite order. Such behavior is in sharp contrast with
the usual quantum representations of mapping class groups where all the Dehn
twists have finite order.

November 28 
Jim Carlson Clay Mathematics Institute 
Jacobians and special periods for cubic surfaces
Cubic surfaces are determined by a period
vector in complex hyperbolic 4space. We present
some results on the nature of the intermediate Jacobian
for the associated cubic threefold when the ratios of
the period vector lie in certain algebraic number fields.
In particular, we show how to construct cubic surfaces
from certain totally real quintic fields. This is joint
work with Domingo Toledo.

December 5 
Aaron Bertram University of Utah 
Tropical plane curves (or what to do when you can't subtract)
This will be an easy introduction to tropical plane
curves, configurations of "general" points in the plane and
a proposal for what an affine cover should look like.

Current Seminar Archive of past talks
Max Dehn Seminar is organized by Mladen Bestvina, Ken Bromberg, Patrick Reynolds,
Jing Tao, Domingo Toledo, and Kevin Wortman.
This web page is maintained by Patrick Reynolds and Jing Tao.