Spring 2016

** Organizers: Gennadi Kasparov, Ioana
Suvaina, ****Rares Rasdeaconu**

** Fridays,
3:10-4:00pm in SC 1310 (unless otherwise noted) **

**Friday, February 5th**

__Speaker:__** Kun Wang,
Vanderbilt University**

__Title____:__** Topological rigidity
for closed aspherical manifolds fibering over the unit
circle** ** **

__Abstract__**: **The Borel conjecture
in manifold topology predicts that every closed aspherical
manifold is

topologically rigid, i.e. every homotopy equivalence between
any two closed aspherical manifolds

is homotopic to a homeomorphism. There are variants of the
Borel conjecture, such as the simple

Borel conjecture and the bordism Borel conjecture,
corresponding to other types of topological rigidity.

In this talk, I consider topological rigidity for closed
aspherical manifolds that fiber over the unit circle.

We show that, in dimensions greater than or equal to 5, both
the simple Borel conjecture and the

bordism Borel conjecture hold for such an aspherical manifold,
provided the fundamental group

of the fiber belongs to a large class of groups, including
Gromov hyperbolic groups, CAT(0) groups,

and lattices in virtually connected lie groups. The main
ingredients in proving this rigidity result

are some general results that we obtain in algebraic
L-theory. These results also have some applications

to the Novikov conjecture.

** Friday, February 12th**

__Speaker:__** Matthieu
Jacquemet, Vanderbilt University**

__Title____:__** Around hyperbolic
Coxeter polyhedra I** **
**

__Abstract__**: **Unlike their
spherical and Euclidean cousins, hyperbolic Coxeter polyhedra
do not exist

any more in higher dimensions, and are far from being
classified. In this first talk, we intend to give

a survey on their existence and classification. No particular
background will be assumed.

** Friday, February 19th**

__Speaker:__** Matthieu
Jacquemet, Vanderbilt University**

__Title____:__** Around hyperbolic
Coxeter polyhedra II** **
**

__Abstract__**: **In this second talk,
we shall discuss recent results related to two natural classes
of

hyperbolic polyhedra : simplices, and Coxeter cubes. It time
permits, we shall outline a couple

of open problems which could be attacked by using these new
results.

Old Seminar Web-Pages: Fall 2009, Fall
2010