The hyperbolic geometry seminar is based at the Graduate Center of the City University of New York (365 5th Ave, New York, NY 10016). All are welcome. It is run as a hybrid seminar with in-person talks. For those who want to zoom-in doors 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 one of the organizers listed below. The zoom link for an upcoming seminar is included in the weekly email list.
Tuesdays 2:45pm–3:45pm, room C415A. (C-level in the basement)
September 15: Matthew Stover (CUNY, Graduate Center)
Title: Rigidity of the moduli space of cubic surfaces
Abstract: This talk will be on joint work with Gregorio Baldi, Benson Farb, and Ariyan Javanpeykar showing that the moduli space of smooth complex cubic surfaces in CP^3 is trivial. This is analogous to classical theorems for the moduli space of Riemann surfaces of genus g, etc. The proof uses an incomplete complex hyperbolic uniformization studied by Carlson and Toledo and connections with a certain Artin group, which both open the door to techniques from geometric topology.
September 22: Jayadev Athreya (Fordham U.)
Title: Pisot Pseudo-Anosov Maps and Eigenfunctions
Abstract: In joint work with Nicolas Bedaride, Pat Hooper, and Pascal Huber, we use ideas of Furstenberg and Veech to connect results about weak mixing properties of flows on translation surfaces to ergodic properties of linear flows on translation prisms, and use this to obtain several results about unique ergodicity of these prism flows and related billiard flows. We construct explicit eigenfunctions for translation flows in pseudo-Anosov directions with Pisot expansion factors, and use this construction to build explicit examples of non-ergodic prism flows, and non-ergodic billiard flows in right prisms over regular n-gons for n=7,9,14,16,18,20,24,30. In this talk, we will focus on the explicit construction, and speculate on potential connections to Cannon-Thurston maps, inspired by some similarities in pictures.
Note: Jayadev is also giving a colloquium talk on this day at 4:15 in the math commons room.
September 29: No seminar
October 6:
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October 13: No seminar (CUNY on Monday schedule)
October 20: Casey Whitney (CUNY, Graduate Center)
Title: Shear coordinates for infinite type surfaces with a bounded ideal triangulation
Abstract: Given an ideal triangulation of a Riemann surface, there is a relationship between adjacent triangles called the shear. Two adjacent triangles on the surface lift to adjacent ideal triangles in H. The shear between two ideal triangles in H is the signed displacement between the orthogonal projections of the non-shared vertices onto the shared edge. Quasiconformal maps change the shears between adjacent triangles, up to homotopy. We wish to identify what types of surfaces admit such a triangulation and which changes of shear coordinates correspond to quasiconformal deformations. We show that for infinite type punctured surfaces that admit a bounded ideal triangulation, there exists a real analytic parametrization of Teichmuller space by these shear coordinates. This is joint work with Dragomir Saric.
October 27: Dongryul Kim (IAS)
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Note: Dongryul will also give a talk in the Geometry and Topology seminar at 4:15pm. The talks are independent.
November 3: Nicholas Miller (Villanova U.)
November 10: Chenxi Wu (U. of Wisconsin)
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November 17: Abdul Zalloum (Queens U.)
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November 24: No seminar (Thanksgiving week)
December 1: Cormac O'Sullivan (CUNY, Graduate Center and Bronx Community College)
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December 8:
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
Matthew Stover (CUNY, Graduate Center) Email: mstover@gc.cuny.edu
Nick Vlamis (CUNY, Graduate Center and Queens College) Email: nvlamis@gc.cuny.edu
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 of areas 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).