Starting in Spring 2023 the seminar will go back to in-person talks. We will also attempt to run the seminar as hybrid using zoom. Zoom doors will open a few minutes before the seminar for chatter and self provided coffee, tea, beer, wine, cocktail, aperitif, digestif, cheese, and snacks depending on your time zone and predilection. If you would like to be put on the email list contact Ara Basmajian (abasmajian@gc.cuny.edu). The zoom link for the upcoming seminar will be included in the weekly mailing to the email list.
Tuesdays 2:45pm–3:45pm, room 5417.
Organizers
Ara Basmajian (CUNY, Graduate Center and Hunter College)
Email: abasmajian@gc.cuny.edu
Dragomir Saric (CUNY, Graduate Center and Queens College)
Email: dragomir.saric@qc.cuny.edu
Nick Vlamis (CUNY, Graduate Center and Queens College)
Email: nvlamis@gc.cuny.edu
February 11: Melkana-Brakalova-trevithick (Fordham U.)
Title: When the circular dilatation at a point equals one
Abstract: I will discuss asymptotic homogeneity/conformality of a q.c. mapping/ $\mu$-homeomorphism at a point and applications.
February 18: (No seminar, Monday schedule)
February 25: (No seminar)
March 4: (No seminar)
March 11: Changji Chen (University of Montreal)
Title: On low degree homology of the Deligne-Mumford compactification of the moduli space via Morse theory
Abstract: For a set of closed geodesics on a point in the Teichmüller space, we consider the set of differentials of the geodesic-length functions in the cotangent space, and study the rank. It is equivalent if one replaces differentials by the Weil-Petersson gradient vectors in the tangent space by duality. We show that the rank has a lower bound depending on the dimension of the Teichmüller space.
Based on the fact that the sys_T functions, defined as a family of weighted exponential averages of all geodesic-length functions, are Morse on the Deligne-Mumford compactification, we will find that the boundedness of the rank implies an isomorphism of low degree rational homology groups between the Deligne-Mumford boundary and the compactification.
March 18: David Aulicino (CUNY, Graduate Center and Brooklyn College)
Title: Connected Components of Branched Cyclic Covers of Strata
Abstract: We consider generic translation surfaces of positive genus with marked points. Moduli spaces of translation surfaces are naturally stratified by the angles at their cone points - equivalently orders of the zeros of an Abelian differential. These strata are not necessarily connected, but the connected components were classified by Kontsevich-Zorich. We consider covers of these surfaces branched over the marked points such that the monodromy of every element in the fundamental group lies in a finite cyclic group. We classify connected components of these covers by introducing invariants similar to the spin invariant of Kontsevich-Zorich. Interestingly, unlike the case of strata, there are branching configurations that always result in a non-connected component. All necessary background will be presented. Time permitting, we will present an application to computing Siegel-Veech constants. This is joint work with Aaron Calderon, Carlos Matheus, Nick Salter, and Martin Schmoll.
March 25: (No seminar, Colloquium)
Title:
Abstract:
April 1: (No seminar)
April 8: (No seminar)
April 15: (No seminar, Spring break)
April 22: (No seminar)
April 29: Ilya Kapovich (CUNY, Graduate Center and Hunter College)
Title: Hausdorff dimension and attracting laminations for free group automorphisms
Abstract: Motivated by a classic theorem of Birman and Series about the set of complete simple geodesics on a hyperbolic surface, we study the Hausdorff dimension of the set of endpoints in $\partial F_r$ of some abstract algebraic laminations associated with free group automorphisms. Thus for a fully irreducible automorphism of $F_r$ and more generally for any exponentially growing automorphism of $F_r$ the set of endpoints associated with its attracting laminations has Hausdorff dimension $0$. We discuss some open questions and related results, particularly concerning the Cannon-Thurston map and the set of non-conical limit points in free-by-cyclic and Kleinian groups context.
May 6: Mingkun Liu (Université Paris 13 Paris Nord)
Title: Length spectra of random hyperbolic surfaces and random graphs
Abstract: After a brief historical review, I will explain how to pick a (uniform) random hyperbolic surface of genus g. After that, we will focus on the length spectrum. More specifically, we will look at short closed geodesics on a random hyperbolic surface of genus g. It turns out that, when g is big, the lengths of these geodesics are distributed just like the short cycles in a large random graph. This is a joint work with Simon Barazer and Alessandro Giacchetto.
HISTORY OF THE HYPERBOLIC GEOMETRY SEMINAR : The hyperbolic geometry seminar has been running continuously since Fall 2008. In the early years it ran mostly as a student seminar with some research talks interspersed. The seminar topics span a wide range including hyperbolic and conformal geometry, geometric structures on manifolds, low dimensional topology, geometric group theory, and many others.
Past organizers have been Youngju Kim (2008-2010), Viveka Erlandsson (2010-2013), Chris Arettines (2013-2015), Blanca Marmolejo (2015-2017), and Daniel White (2017-2019).