Columbia Geometric Topology Seminar

Spring 2014

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

Spring 2014

Date Speaker Title
January 24 Organizational meeting 1:15pm Room 520
January 31 Jason Behrstock Higher dimensional filling and divergence for mapping class groups.
February 7 BoGwang Jeon Hyperbolic three maniflds of bounded volume and trace field degree II
February 14 Mina Teicher Line Arrangements -Topology, Combinatorics and application to Algebraic Surfaces
February 21 Bill Menasco Short distances in the curve complex
February 28 Adam Levine Non-orientable surfaces in homology cobordisms
March 7 No GT Seminar  
March 14 Jingyin Huang Quasi-isometry classification of right-angled Artin group with finite outer automorphism group
March 21 No Seminar Spring Break
March 28 Marc Culler Character varieties of knot complements
April 4 Tarik Aougab Minimally intersecting filling pairs on surfaces
April 11 Tom Church A survey of representation stability
April 18 No Seminar  
April 25 Matthew Day An infinite presentation for the Torelli subgroup IA_n of the automorphism group of a free group
May 2 David Fisher Quasi-isometric embeddings: rigidity and examples 
May 9, Room 622 Math Adam Giambrone Semi-Adequate Link Diagrams and Hyperbolic Volume Estimates

Fall 2014

Date Speaker Title
TBA Jane Gilman TBA
TBA David Shea Vela-Vick TBA



January 31: Jason Behrstock: “Higher dimensional filling and divergence for mapping class groups.”
Abstract: We will discuss filling and divergence functions. We will describe their behaviors for mapping class groups of surfaces and show that these functions exhibit phase transitions at the rank, in analogy to the corresponding result for symmetric spaces. This work is joint with Cornelia Drutu.

February 7: BoGwang Jeon: “Hyperbolic three maniflds of bounded volume and trace field degree II”
Abstract:A year ago, in the same seminar (, I proposed a way to attack the conjecture that there are only finitely many hyperbolic three manifolds of bounded volume and trace field degree. In this talk, I will go over the previous talk and present further results and related questions. No further background will be necessary but it will be good to know about Thurston's Dehn filling theorem.

February 14: Mina Teicher “Line Arrangements -Topology, Combinatorics and application to Algebraic Surfaces”
Abstract: In this talk Topology means Fundamental Group of the complement of the line arrangement, and Combinatorics means the Lattice of the arrangement or its Graph. I will review the history of the problem of Topology vs. Combinatorics of line arrangements, give the state of the art as well as reporting on work in Progress. I'll conclude with applications to Topology of Algebraic Surfaces.

February 21: Bill Menasco “Short distances in the curve complex”
Abstract: We will give a preliminary report on recent joint work with Dan Margalit and Joan Birman. The focus is an algorithm for determining whether a filling pair of curves in an orientable closed surface of genus greater than 1 has distance 3, 4, 5 or bigger. The algorithm is a natural generalization of John Hempel's distance 3 algorithm (unpublished) and a significant improvement of the previously know algorithms of Leasure and Shackleton for determining the distance between two curves in the curve complex. As an application of the algorithm we will give newly discovered distance 4 pairs of curves in genus 2 and 3 surfaces.

February 28: Adam Levine: “Non-orientable surfaces in homology cobordisms”
Abstract:We study the minimal genus problem for embeddings of closed, non-orientable surfaces in a homology cobordism between rational homology spheres, using obstructions derived from Heegaard Floer homology and from the Atiyah-Singer index theorem. For instance, we show that if a non-orientable surface embeds essentially in the product of a lens space with an interval, its genus and normal Euler number are the same as those of a stabilization of a non-orientable surface embedded in the lens space itself. This is joint work with Danny Ruberman and Saso Strle.

March 14: Jingyin Huang “Quasi-isometry classification of right-angled Artin group with finite outer automorphism group”
Abstract: Let G and G' be two right-angled Artin groups with finite outer automorphism group, we show they are isomorphic iff they are quasi-isometric. If we only assume Out(G) is finite, then G' can be realized as a subgroup of finite index in G, and there is a correspondence between such G' and compact convex subcomplexes in the Salvetti complex of G, which can be thought as a nice fundamental domain for G'.

March 28: Marc Culler “Character varieties of knot complements
Abstract: I will survey some known connections between knot invariants and character varieties, framed in terms of a computable object called the PE character variety, which includes the SU(2) character variety but is defined in terms of the SL(2,C) character variety.

April 4: Tarik Aougab: “Minimally intersecting filling pairs on surfaces”
Abstract: Let S_{g} denote the closed orientable surface of genus g. We show the existence of exponentially many mapping class group orbits of pairs of simple closed curves on S_{g} which fill the surface, and intersect minimally amongst all filling pairs. We will demonstrate the main idea of the construction, and discuss applications of minimally intersecting filling pairs to understanding how the coarse geometry of the curve complex explicitly depends on the topology of the underlying surface.

April 11: Tom Church: “A survey of representation stability”
Abstract: I will give a gentle survey of the theory of representation stability, viewed through the lens of its applications. These applications include: homological stability for configuration spaces of manifolds; understanding the stable (and unstable) homology of arithmetic lattices; Hecke eigenclasses in stable mod-p cohomology; uniform generators for congruence subgroups and "congruence" subgroups; and distributional stability for random squarefree polynomials over finite fields.

April 25: Matthew Day: “An infinite presentation for the Torelli subgroup IA_n of the automorphism group of a free group”
Abstract: I will describe joint work with Andy Putman, in progress, in which we verify the group presentation described in the title. �This infinite presentation is a "finite L-presentation", meaning that it has finitely many generators, finitely many basic relations, and a sufficient set of relations is given by the orbit of the basic relations under the action of a finitely generated monoid. �The proof involves the action of Aut(F_n) on a curve complex analog, and also uses the theory of group extensions. �As corollaries, we obtain several results about the second homology H_2(IA_n).

May 2: David Fisher: “Quasi-isometric embeddings: rigidity and examples”
Abstract: We study quasi-isometric embeddings of higher rank symmetric spaces into one another. This generalizes both Mostow-Margulis rigidity and the rigidity of self-quasi-isometries of these spaces (Kleiner-Leeb, Eskin-Farb). I will present some rigidity results (which were to be expected) as well as some surprising examples. I will end the talk with several open problems. This is joint work with Kevin Whyte.

May 9: Adam Giambrone: “Semi-Adequate Link Diagrams and Hyperbolic Volume Estimates”
Abstract: In this talk we will explore some ways to bound the volume of the complement of certain hyperbolic, semi-adequate links. First, we find volume bounds that can be expressed in terms of two diagrammatic quantities: the twist number and the number of certain alternating tangles in a semi-adequate link diagram. Second, we express these volume bounds in terms of a single coefficient of the colored Jones polynomial of the link. Consequently, we are able to provide a number of families of links that satisfy a Coarse Volume Conjecture. The two main families of links that we will consider are closures of braids and plat closures of braids.

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Previous semesters:

Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, 2010/11, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006.

Other area seminars.

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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.