The Lafayette/Lehigh Geometry and Topology Seminar


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Spring Semester 2009

 

 

This spring’s talks are organized into a mini-conference that will meet on Saturday, March 21, 2009

 

All talks will be on the second floor of Pardee Hall at Lafayette College.  Directions to Lafayette College can be found here, and a campus map can be found here.  Visitors can either park in front of Pardee Hall and enter through the door facing the quad or can park at the Markle Deck.  From Markle Deck, cross High street and head towards the quad (the library, the building with a lot of glass, should be on your right).  Cross the quad; Pardee will be in front of you and slightly to the left.  Enter through the door facing the quad.

 

 

Schedule of Events: There will be coffee and snacks at 9:30, with talks starting at 10:00.  Lunch is provided, and the seminar will end around 3:00

 

 

 

9:30 – 10:00

 

Coffee and snacks

 

 

10:00 – 10:50

Jie Qing

(UCSC, currently at IAS) 

 

Title:  Finiteness and gap theorems in conformal geometry

 

Abstract:  We will discuss a diffeomorphism finiteness and gap theorem for Bach flat 4-manifolds in conformal geometry.  Following the idea in the finiteness theorem of Anderson and Cheeger, our theorem is based on a construction of a bubble tree of the degeneration of metrics.

 

11:00 – 11:50

 

Anna Wienhard (Princeton)

 

 

Title:  Domains of discontinuity for Anosov representations

 

Abstract:  Let Γ be the fundamental group of a closed surface of genus g ≥ 2 and ρ: Γ   G a representation into a semisimple Lie group.  When does there exists a parabolic subgroup P and a non-empty open subset Ω in G/P such that  Γ acts properly discontinuously on Ω with compact quotient?

 

A positive answer to this question was known for some special classes of representations, e.g. quasi-Fuchsian representations of Γ into PSL(2,C) or convex representations into PSL(3,R).

 

We construct such domains of discontinuity for a much bigger class of representations, so-called Anosov representations, which are characterized by certain dynamical properties. This class includes in particular all “higher” Teichmüller spaces.

 

This is joint work with Olivier Guichard.

 

 

12:00 – 1: 00

 

Lunch (provided)

 

 

1:10 – 2:00

Lucas Sabalka (Binghamton University)

 

Title:  Generalized Expanders

 

Abstract:   Tessera and Ostrovskii have independently introduced a generalized notion of expander in terms of probability measures on metric spaces.  In joint work with Jerry Kaminker, we analyze certain classes of these generalized expanders.  In this context we study, among other results, the obstruction to being able to uniformly embed a metric space into a Hadamard manifold.

 

2:10 – 3:00

Dave Futer

(Temple University)

 

Title:  The geometry of unknotting tunnels

Abstract:  Let K be a knot that lives in a closed manifold such as S3.   Then an unknotting tunnel for K is an arc τ running from K to K, with the property that the complement of K and τ is a handlebody.  Equivalently, the unknotting tunnel defines a genus-2 Heegaard splitting of the complement of K.

 

In the generic situation where the complement of K is hyperbolic, we can ask a number of geometric questions about the tunnel. The following questions have been open since the mid 1990s: Is τ isotopic to a geodesic? Is it isotopic to an edge of the canonical triangulation? Can τ be arbitrarily long?

 

I will present some recent work, joint with Jessica Purcell, that answers these three questions if the knot K is created by long Dehn filling.



 

 

Past seminar schedules:

 

2007-2008 Academic Year

2006-2007 Academic Year

2005-2006 Academic Year

2004-2005 Academic Year

2003-2004 Academic Year

2002-2003 Academic Year

 


For further information, contact Ethan Berkove at berkovee at lafayette dot edu.


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