January 30th: Hugo Parlier (University of Luxembourg)
Joint meeting with CUNY Geometry and Topology Seminar. Please note this meeting is in room 3212 at 4:15pm.
Title: Families of identities on hyperbolic surfaces
Abstract: There are a number of so-called “identities” which are equations which relate the lengths of geodesics on a hyperbolic surface to some geometric quantity. Earlier versions of these are due to Basmajian and McShane, the latter of which was generalized by Mirzakhani and used in a spectacular fashion. This talk will be about a new family of identities which generalize Basmajian’s identity, and interpolate in some sense between the identities of Basmajian and McShane. This is joint work with Ara Basmajian and Ser Peow Tan.
Link to CUNY Geometry and Topology Seminar: Geometry and Topology Seminar
February 6th: Dragomir Saric (CUNY Graduate Center and Queens College)
Title: Thurston boundary for infinite surfaces via geodesic currents
Abstract: We introduce Thurston boundary for Teichmüller spaces of infinite surfaces using geodesic currents. Our construction uses the Liouville map from Teichmüller space into geodesic currents which was already used by Bonahon to give an alternative description of Thurston boundary for closed surfaces. The novelty of our approach is the need of introducing a new topology on geodesic currents which we called the uniform weak* topology. The uniform weak* topology makes the Liouville map an embedding and the projectivization of the image of Teichmüller space has the space of projective bounded measured laminations as its boundary. The bordification of Teichmüller space is not a compactification since Teichmüller space of infinite surface is not even locally compact. However, the mapping class group action extends by continuity to Thurston boundary. This is a joint work with F. Bonahon.
February 13th: David Futer (Temple University)
Joint meeting with CUNY Geometry and Topology Seminar.
Title: Veering Triangulations: theory and experiment
Abstract: Every fibered hyperbolic 3-manifold M has a canonically associated veering triangulation. This triangulation (technically, an ideal triangulation of a certain surgery parent of M) was introduced by Agol, and has nice combinatorial and dynamical properties. The question is: how much geometry does it encode? I will describe the results of a large-scale computational experiment that provides some intriguing answers. Then, I will promote one of the experimental results to a theorem, outlining a proof that generic mapping classes give rise to non-geometric veering triangulations. The proof relies on results and ideas by Gadre and Maher. This is joint work with Sam Taylor and Will Worden.
February 20th: No meeting (CUNY Monday schedule)
February 27th: No meeting (Scheduling conflict)
March 6th: Dragomir Saric (CUNY Graduate Center and Queens College)
Title: Thurston boundary for infinite surfaces via geodesic currents (continued)
March 13th: No meeting (Faculty meeting and colloquium)
March 20th: Irene Pasquinelli (Durham University)
Title: Deligne-Mostow lattices and cone metrics on the sphere
Abstract: Finding lattices in PU(n,1) has been one of the major challenges of the last decades. One way of constructing a lattice is to give a fundamental domain for its action on the complex hyperbolic space.
One approach, successful for some lattices, consists of seeing the complex hyperbolic space as the configuration space of cone metrics on the sphere and of studying the action of some maps exchanging the cone points with same cone angle.
March 27th: No meeting (Scheduling conflict)
April 3rd: No meeting (Spring recess)
April 10th: Ara Basmajian (CUNY Graduate Center and Hunter College)
Title: Collar neighborhoods of geodesics and extremal length calculations
Abstract: A collar neighborhood of a closed geodesic in a hyperbolic surface is an open neighborhood of the geodesic which is topologically an annulus. It is well-known that a simple closed geodesic on a hyperbolic surface has a natural (or standard) collar. The outstanding feature of the natural collar is that its size depends on local data, namely its size only depends on the length of the geodesic. Using this collar one can make extremal length calculations of curve families that are transverse to the geodesic in terms of its length.
In this talk we define a new type of collar which we call a non-standard collar. The non-standard collar also depends on local data where the local data now includes the size of a pair of pants whose boundary contains the given geodesic. Using the non-standard collar we are able to improve estimates on the extremal length of curve families that are transverse to the geodesic and give a number of applications to infinite type surfaces. This is joint work with Hrant Hakobyan and Dragomir Saric.
This talk will consist of two parts. The first part will be a basic introduction to the notions of extremal length and modulus of a curve family. The second part will be devoted to extremal length calculations and their interplay with hyperbolic geometry.
April 17th: Ara Basmajian (CUNY Graduate Center and Hunter College)
Title: Collar neighborhoods of geodesics and extremal length calculations (part 2)
April 24th: No meeting (Conference in honor of James Simons)
Link to conference website: At Most 3D Real Fluids & At Least 3D Complex Manifolds
May 1st: Ara Basmajian (CUNY Graduate Center and Hunter College)
Title: Collar neighborhoods of geodesics and extremal length calculations (part 3)
May 8th: Joseph Fera (Lehman College)
Title: Exceptional Points for cocompact Fuchsian groups
Abstract: Let G be a cocompact Fuchsian group acting on the hyperbolic plane H. If G covers a compact hyperbolic surface of genus g (at least 2), then almost every Dirichlet region for G has 12g-6 sides. In this talk, we discuss the exceptional points for G, i.e., the points in H associated to Dirichlet regions for G with strictly less than 12g-6 sides. More specifically, we show that uncountable many exceptional points exist for any cocompact group. We also define and prove the existence of higher order exceptional points for any such group. Current results and further questions will be included as time permits.
May 15th: Ara Basmajian (CUNY Graduate Center and Hunter College)
Title: Computing extremal lengths for pairs of pants
Diversity and Inclusion at the GC