Geometry and Topology Seminar

2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021

Current contacts: Dave Futer, Matthew Stover, or Sam Taylor.

The Seminar usually takes place on Fridays at 10:40 AM via Zoom (please contact the seminar organizers for the Zoom link), not in Room 617 on the sixth floor of Wachman Hall.

• Friday January 29, 2021 at 10:40, over Zoom

  Isospectral hyperbolic surfaces of infinite genus

  Federica Fanoni, University of Paris

  Abstract: Two hyperbolic surfaces are said to be (length) isospectral if they have the same collection of lengths of primitive closed geodesics, counted with multiplicity (i.e. if they have the same length spectrum). For closed surfaces, there is an upper bound on the size of isospectral hyperbolic structures depending only on the topology. We will show that the situation is different for infinite-type surfaces, by constructing large families of isospectral hyperbolic structures on surfaces of infinite genus.

• Friday February 12, 2021 at 10:40,

  Constructing examples and non-examples of jigsaw pseudomodular groups

  Carmen Galaz-Garcia
  University of California, Santa Barbara
   
  Consider a discrete subgroup H of PSL(2,R) and its action on IH^2 the upper half-plane model of the hyperbolic plane. The cusp set of H is the set of points in the boundary at infinity of IH^2 fixed by its parabolic elements. For example, the cusp set of PSL(2,Z) is QU{oo}. A natural question is: how strong is the cusp set as an invariant? More precisely, if H has cusp set  QU{oo} , is it commensurable with PSL(2,Z)? A negative answer was provided by Long and Reid in 2001 by constructing finitely many examples of pseudomodular groups. In 2016 Lou, Tan and Vo produced two infinite families of pseudomodular groups via the jigsaw construction. In this talk we will construct a third family of pseudomodular groups obtained with the jigsaw construction and also show that "many" of the simplest jigsaw groups are not pseudomodular. 
   
   
  

• Friday February 19, 2021 at 10:40, over Zoom

  A polynomial invariant for veering triangulations

  Sam Taylor

  Temple University

  Veering triangulations form a rich class of ideal triangulations of cusped hyperbolic manifolds that were introduced by Agol and have connections to hyperbolic geometry, Teichmuller theory, and the curve complex. In this talk, we introduce a polynomial invariant of a veering triangulation that, when the triangulation comes from a fibration, recovers the Teichmuller polynomial introduced by McMullen. We show that in general, the polynomial determines a (typically non-fibered) face of the Thurston norm ball and that the classes contained in the cone over this face have representatives that are carried by the veering triangulation itself.

  This is joint work with Michael Landry and Yair Minsky.
  

• Friday February 26, 2021 at 10:40, over Zoom

  Cannon-Thurston maps: to exist or not to exist

  Radhika Gupta, Temple University

  
  Consider a hyperbolic 3-manifold which is the mapping torus of a pseudo-Anosov on a closed surface of genus at least 2. Cannon and Thurston showed that the inclusion map from the surface into the 3-manifold extends to a continuous, surjective map between the visual boundaries of the respective universal covers. This gives a surjective map from a circle to a 2-sphere. In this talk, we will explore what happens when we consider the mapping torus of a surface with boundary, which is not hyperbolic but CAT(0) with isolated flats.

• Friday March 5, 2021 at 10:40, over Zoom

  Geodesic currents and the smoothing property

  Didac Martinez-Granado, UC Davis

  Abstract: Geodesic currents are measures that realize a closure of the

  space of curves on a closed surface.
  Bonahon introduced geodesic currents in 1986, showed that geometric
  intersection number extends to geodesic currents
  and realized hyperbolic length of a curve as intersection number with a
  geodesic current associated to the hyperbolic structure.
  Since then, other functions on curves have been shown to extend to
  geodesic currents. Some of them extend as intersection numbers, such as
  negatively curved Riemannian lengths (Otal, 1990)
  or word length w.r.t. simple generating sets of a surface group
  (Erlandsson, 2016). Some other functions aren't intersection numbers but
  extend continuously (Erlandsson-Parlier-Souto, 2016), such as word
  length w.r.t. non-simple generating sets or extremal length of curves.
  In this talk we present a criterion for a
  function on curves to extend continuously to geodesic currents.
  This is joint work with Dylan Thurston.

• Friday March 12, 2021 at 11:00, over Zoom

  RAAGs in MCGs

  Ian Runnels, University of Virginia

  Abstract: Inspired by Ivanov's proof of the Tits alternative for mapping class groups via ping-pong on the space of projective measured laminations, Koberda showed that right-angled Artin subgroups of mapping class groups abound. We will outline an alternate proof of this fact using the hierarchy of curve graphs, which lends itself to effective computations and stronger geometric conclusions. Time permitting, we will also discuss some applications to the study of convex cocompact subgroups of mapping class groups.

• Friday April 9, 2021 at 14:00, over Zoom

  Marissa Loving tba

  Marissa Loving, Georgia Tech

  Seminar time TBA Title/abstract TBA

2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021