Geometry/Topology Seminar
Winter 2015
Thursdays (and sometimes Tuesdays) 34pm, in
Eckhart 308

 Thursday February 5 at 34pm in Eck 308
 Nathan Dunfield, University of Illinois at UrbanaChampaign
 Certifying the Thurston norm via twisted homology

Abstract: From the very beginning of 3manifold
topology, a fundamental task has been to find the simplest
surface in a given 2dimensional homology class, e.g. the
Seifert genus of a knot in the 3sphere. The behavior of the
minimal topological complexity as the homology class varies
is encapsulated in the Thurston norm. In this talk, I will
discuss tools for proving that a particular surface has
minimal genus. These are generalizations of the classical
Alexander polynomial, but are defined using homology with
coefficients twisted by some finitedimensional
representation of the fundamental group of the manifold. I
will discuss recent work with Ian Agol on situations where
using representations coming from hyperbolic geometry
suffices to provide such certificates. If time permits, I
will sketch how all of this relates to fundamental questions
about the computational complexity of finding the Thurston
norm. Only basic facts about manifolds and homology will be
assumed.

 Thursday February 12 at 34pm in Eck 308
 Juliette Bavard, Institut de Mathematiques de Jussieu
 About a big mapping class group

Abstract: The mapping class group of the complement
of a Cantor set in the plane arises naturally in dynamics.
To get informations about this "big mapping class group", we
can look at its action on a hyperbolic space: the ray graph.
In this talk, I will explain why this ray graph has infinite
diameter and is hyperbolic. I will then exhibit an element
of the big MCG which has a loxodromic action on the ray
graph, and explain why this element is useful to construct
non trivial quasimorphisms on the group.

 Tuesday March 3 at 1:302:30pm in Eck 202
 Holger Reich, Freie Universitat Berlin
 TBA

Abstract: TBA

 Tuesday March 3 at 34pm in Eck 308
 Lev Buhovsky, Tel Aviv University
 TBA

Abstract: TBA

 Tuesday March 10 at 34pm in Eck 308
 Andrzej Szczepanski, Gdansk
 TBA

Abstract: TBA

 Thursday March 12 at 34pm in Eck 308
 David Dumas, UIC
 TBA

Abstract: TBA
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