Organizers

Nathan Broaddus
Mike Davis

Links

OSU Math Department

Participanting Faculty

Dan Boros
Sergei Chmutov
Dan Burghelea
Jim Fowler
Matthew Kahle
Thomas Kerler
Raeyong Kim
Jean-François Lafont
Guido Mislin
Crichton Ogle
Izhar Oppenheim
Bobby Ramsey

Previous Years

2015-2016
2014-2015
2013-2014
2012-2013
2011-2012
2010-2011

Autumn 2013
Thursday, September 12, 2012 at 3pm in CH (Cockins Hall) 240

Mike Davis, OSU

Aspherical manifolds that cannot be triangulated

Abstract

By a result of Manolescu  there are  topological closed n-manifolds that cannot be triangulated for each n greater than or equal to 5.  We show  that for n greater than or equal to 6, we can choose such manifolds to be aspherical.  This is joint work with jim Fowler and Jean Lafont.

Thursday, September 19, 2013 at 1:50 pm in CH (Cockins Hall) 240

Kathyrn Mann, University of Chicago

Components of representation spaces

Abstract

Let G be a group of homeomorphisms of the circle, and \Gamma the fundamental group of a closed surface.  The representation space Hom(\Gamma, G) is a basic example in geometry and topology: it parametrizes circle bundles over the surface with structure group G, and actions of \Gamma on the circle with regularity given by G.  A remarkable theorem of W. Goldman says that for G = PSL(2,R), the components of Hom(\Gamma, G) are completely determined by the Euler number, a classical invariant.  By contrast, the space Hom(\Gamma, Homeo+(S^1)) is relatively unexplored -- in fact it is an open question whether it has finitely many or infinitely many components.
In this talk, I'll motivate the study of representation spaces, and then report on recent work and new tools to distinguish connected components of Hom(\Gamma, Homeo+(S^1)).  In particular, this work gives a new lower bound on the number of components (more than are distinguished by the Euler number alone) and identifies many representations which exhibit surprising rigidity.

Thursday, September 26, 2013 at 1:50 pm in CH (Cockins Hall) 240

David Simmons, OSU

Geometry and dynamics of groups acting on Gromov hyperbolic metric spaces

Abstract

In this talk, I will discuss two theorems about groups acting by isometries on Gromov hyperbolic metric spaces. The first theorem is a generalization of a theorem of Bishop and Jones ('97) and Paulin ('97) to this setting. The second is a construction of Patterson-Sullivan measures in a setting where compactness is not assumed. Both theorems are part of an ongoing collaboration with Tushar Das (University of Wisconsin - La Crosse) and Mariusz Urbański (University of North Texas).

Thursday, November 21, 2013 at 1:50 pm in CH (Cockins Hall) 240

Olympia Talelli, University of Athens

On characteristic modules for groups

Abstract

A characteristic module for a group G is a Z-free ZG-module, of finite projective dimension over ZG, with nontrivial elements invariant under the action of G. We present the relation of the characteristic modules to the Gorenstein dimension of G, the generalized cohomological dimension of
G and proper actions of G.

Spring 2014
Thursday, April 17, 2014 at 1:50 pm in MA 317

Tam Nguyen Phan, University of Binghamton

Ends of finite volume, negatively curved manifolds

Abstract

Let M be an oriented, noncompact, complete, Riemannian manifold. Gromov proved that if the sectional curvature of M negative and bounded, and if the volume of M is finite, then M is homeomorphic to the interior of a compact manifold \overline{M} with boundary B. I will discuss the question what manifold  B can be. I will prove that when M has dimension 4, each boundary component of \overline{M} is aspherical.