Columbia Geometric Topology Seminar

Spring 2012

The GT seminar meets on Fridays in Math. 520, at 1:15PM.
Organizer: Walter Neumann.
Other area seminars. Our e-mail list. Archive of previous semesters

FALL 2011

Date Speaker Title
January 19, 3pm
Room 528
Dani Wise Quasiconvex Subgroups of Relatively Hyperbolic groups
January 20 Everyone Organizational meeting joint with SGGTC seminar
January 27 Jose Luis Cisneros-Molina Geometric elements in algebraic K-Theory
February 3 Tudor Dimofte Non-Abelian Torsion and the Neumann-Zagier Equations
February 10 David Futer The Jones polynomial and surfaces far from fibers
February 17 Craig Hodgson TBA
February 24 TBA TBA
March 2 Elizabeth Denne Transversality theorems for configuration spaces and applications to the "square peg" problem.
March 9 TBA TBA
March 16 Spring Break Spring Break
March 23 Khalid Bou Rabee TBA
March 30 Harriet Moser TBA
April 6 Matthias Kreck TBA
April 13 TBA TBA
April 20 Yi Liu TBA
April 25? Howie Masur Note changed date
April 27 TBA TBA
May 4 TBA TBA
May 11 TBA TBA

 

Abstracts.

January 19. Note room change: Math 528

Dani Wise, “Quasiconvex Subgroups of Relatively Hyperbolic groups ”

Abstract: I will review Bowditch's treatment of a relatively hyperbolic group, and in that context, describe an elegant reformulation of the notion of "relatively quasiconvex subgroup" introduced with Eduardo Martinez-Pedroza. I will then describe work with Hadi Bigdely that applies this criterion to recognize the relative quasiconvexity of a subgroup H in a group G splitting as a graph of groups. The simplest applications revisit beautiful work of Dahmani and others.

January 27

Jose Luis Cisneros-Molina “Geometric elements in algebraic K-Theory”

Abstract: In this talk we show how to represent elements in $K_3(C)$ using homology 3-spheres and hyperbolic 3-manifolds endowed with a representation of their fundamental group. We review some results of Jones and Westbury and the relation of such elements with the Bloch invariant defined by Neumann and Yang.

February 3

Tudor Dimofte “Non-Abelian Torsion and the Neumann-Zagier Equations”

Abstract: I will present an extraordinarily simple formula for the torsion of a hyperbolic 3-manifold M in terms of shape parameters and gluing matrices involved in an ideal triangulation. The torsion appears (for example) as the first subleading correction to the large-N asymptotics of the Kashaev invariant of M. The formula immediately shows that the torsion belongs to the invariant trace field of M. (This is ongoing work with S. Garoufalidis.)

February 10

David Futer “The Jones polynomial and surfaces far from fibers”

Abstract: This talk explores relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement. We also show that certain coefficients of the Jones and colored Jones polynomials measure how far this surface is from being a fiber in the knot complement. This is joint work with Effie Kalfagianni and Jessica Purcell.

Mar 2

Elizabeth Denne “Transversality theorems for configuration spaces and applications to the "square peg" problem.”

Abstract: In joint work with Jason Cantarella and John McCleary, we prove a transversality "lifting property" for compactified configuration spaces. Namely, the submanifold of configurations of points on an arbitrary submanifold of Euclidean space may be made transverse to any submanifold of the configuration space of points in Euclidean space by an arbitrarily small variation of the initial submanifold, as long as the two submanifolds of configuration space are boundary-disjoint. We use this setup to provide proofs of a number of "special inscribed configurations" using differential topology. For instance, there are an odd number of inscribed squares in a generic plane curve, while there is a family of inscribed regular (n+1)-simplices in a generic (n-1)-sphere.

Other relevant information.

Previous semesters:

Fall 2011, 2010/11, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006.

Other area seminars.

Our e-mail list.

Announcements for this seminar, as well as for related seminars and events, are sent to the GT seminar mailing list. You can subscribe directly or by contacting Walter Neumann.