Geometry/Topology Seminar

Spring 2017

Thursdays (and sometimes Tuesdays) 3-4pm, in Eckhart 308

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• 1/19/17
• 1/26/17
• 2/7/17
• 2/14/17
• 2/22/17
• 3/28/17
• 4/6/17
• 4/20/17
• 4/27/17
• 5/11/17
• 5/30/17
• 6/8/17

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• contacts

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• previous quarters
• F2016
• S2016
• W2016
• F2015
• S2015
• W2015
• F2014
• S2014
• W2014
• F2013
• S2013
• W2013
• F2012
• S2012
• W2012
• F2011
• S2011
• W2011
• F2010
• S2010
• W2010
• F2009
• S2009
• W2009
• F2008
• S2008
• W2008
• F2007
• S2007
• W2007
• F2006
• S2006
• W2006

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• • Tuesday March 28 at 3-4pm in Eck 308
  • Jenny Wilson, Stanford
  • Stability in the second homology of Torelli groups
  • Abstract: In this talk, I will describe stability results for two families of groups, the Torelli groups of automorphisms of free groups, and the Torelli groups of mapping class groups of surfaces with one boundary component. Specifically, I will explain the following statement: the degree-2 integer homology groups of these Torelli groups are centrally stable when viewed as representations of GL_n(Z) or (respectively) Sp_2n(Z). This project uses a framework developed by Putnam, Church-Ellenberg-Farb, and Putnam-Sam. It is joint work with Jeremy Miller and Peter Patzt. (This talk is on a Tuesday.)
• • Thursday April 6 at 3-4pm in Eck 308
  • Dan Margalit, Georgia Tech
  • Fast Nielsen-Thurston Classification
  • Abstract: The Nielsen-Thurston classification says that every homeomorphism of a surface falls into one of three categories: periodic, reducible, or pseudo-Anosov. Given a homotopy class of homeomorphisms (as a product of Dehn twists) a basic problem is to determine its Nielsen-Thurston type. With Balazs Strenner and Oyku Yurttas, we provide a quadratic-time algorithm for this problem. In the talk we will discuss the basic ingredients that go into the problem and give a high-level overview of the solution.
• • Thursday April 20 at 3-4pm in Eck 308
  • Fedor Manin, University of Toronto
  • TBA
  • Abstract: TBA
• • Thursday April 27 at 3-4pm in Eck 308
  • Tam Nguyen-Phan, SUNY Binghamton
  • An analog of the Tits "building" in nonpositive curvature
  • Abstract: Locally symmetric manifolds (of noncompact type) form an interesting class of nonpositively curved manifolds. By Borel-Serre, the thin part of the universal cover of an arithmetic locally symmetric space is homotopically equivalent to the rational Tits building, which is homotopically a wedge of spheres of dimension q-1, where Q is the Q-rank of the locally symmetric space. In general, q is less than or equal to n/2. We show that this is not an arithmetic coincidence in a weaker sense, which is that if M is a noncompact, bounded nonpositively curved manifold with finite volume and no arbitrarily small geodesic loops (so that M is tame), then any nontrivial homology cycle in the thin part of \tilde{M} must have dimension less than or equal to n/2 - 1. For each such cycle, we construct a complex at infinity of dimension less than n/2 that is an analog of the Tits building which we collapse the cycle onto. I will describe how this is done.
• • Thursday May 11 at 3-4pm in Eck 308
  • Kyle Kinneberg, Rice
  • Rigidity for convex-cocompact actions on rank-one symmetric spaces
  • Abstract: According to a classical theorem of Bowen, the limit set of any quasi-Fuchsian action on 3-dimensional hyperbolic space is either a round circle or has Hausdorff dimension strictly greater than 1. In 2005, Bonk and Kleiner established a version of Bowen's result for convex-cocompact actions on real hyperbolic space. In this talk, I'll describe how these results extend to convex-compact actions on non-compact rank-one symmetric spaces. This relies on understanding the metric tangents of PI subsets of sub-Riemannian Carnot groups.
• • Tuesday May 30 at 3-4pm,4:30-5:30pm in Eck 203
  • Jeremey Miller, Purdue
  • TBA
  • Abstract: TBA. Joint with Algebraic Topology seminar. Note that this talk is on Tuesday at 4:30 in Eckhart 203. The 3:00-4:00 portion is a preseminar.
• • Thursday June 8 at 2-3pm in Eck 308
  • Maxime Bourque, Toronto
  • Teichmuller spaces of polygons
  • Abstract: The Teichmuller space of pentagons has a somewhat curious geometry with respect to the Teichmuller metric. This space is complete, uniquely geodesic, homeomorphic to the plane, yet it contains non-convex balls. Nevertheless, it is exhausted by convex geodesic pentagons. In particular, the convex hull of any compact set in this space is compact. I do not know if this holds in the space of hexagons, but some numerical evidence suggests that the same strategy of proof might work.
• • Thursday June 8 at 3:30-4:30pm in Eck 308
  • Kasra Rafi, Toronto
  • Geodesic currents and counting problems
  • Abstract: We show that, for every filling geodesic current, a certain scaled average of the mapping class group orbit of this current converges to multiple of the Thurston measure on the space of measured laminations. This has applications to several counting problems, in particular, we count the number of lattice points in the ball of radius R in Teichmüller space equipped with Thurston's asymmetric metric. This is a joint work with Juan Souto.

Due to the high number of requests, we are no longer accepting speakers via self-invitations.

For questions, contact

• Benson Farb, farb at math.uchicago.edu
• Alex Eskin, eskin at math.uchicago.edu
• Shmuel Weinberger, shmuel at math.uchicago.edu
• Howard Masur, masur at math.uchicago.edu
• Danny Calegari, dannyc at math.uchicago.edu
• David Cohen, dbcohen at math.uchicago.edu
• Andrew Zimmer, andrew.zimmer at math.uchicago.edu