Hyperbolic Geometry Seminar
Location
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.
Time
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
Fall 2023 Schedule (room 5417)
September 12: Daniele Alessandrini (Stevens Institute of Technology)
Title: Domains of discontinuity for Anosov representations
Abstract: The parameter spaces of Anosov representations can usually be seen as deformation spaces of parabolic geometric structures on some closed manifolds, this is due to Guichard-Wienhard and Kapovich-Leeb-Porti. A particularly interesting case is given by the Higher Teichm\"uller Spaces, spaces that generalize the classical Teichm\"uller spaces for higher rank Lie groups.
In this talk we will present a general structure theorem about the topology of such closed manifolds, and we will describe this topology explicitly in some interesting cases.
September 19: Changjie Chen (Brown University)
Title: $C^2$-Morse functions on $\overline{\mathcal M}_{g,n}$ and a distribution theorem on low index critical points
Abstract: In 2003, Akrout proved that the systole function is topologically Morse on the moduli space $\mathcal M_{g,n}$ of Riemann surfaces. However, classical Morse theory cannot be applied. In this talk, we construct a series of $C^2$-Morse functions on the Deligne-Mumford compactification of $\mathcal M_{g,n}$ that converges to systole and compare critical points of these functions to those for systole. We show that all low index critical points for these functions exist in the Deligne-Mumford boundary $\partial\mathcal M_{g,n}$ for large g or n, which implies all low degree handles in the Morse handle decomposition appear in the boundary. We also give a classification of all index 0, 1 and 2 critical points.
September 26: Nicholas Vlamis (CUNY)
Title: Big mapping class groups that are small
Abstract: The mapping class group of a 2-manifold is big if the 2-manifold is of infinite type (i.e. its fundamental group is not finitely generated). Big mapping class groups are big in the sense that they are uncountable groups and, as topological groups, are not locally compact. Despite this, they can be geometrically small. We will discuss various ways that a group may be geometrically small and the various classes of big mapping class groups that satisfy these smallness conditions. Some of the work discussed is joint with Justin Lanier.
October 3: Dragomir Saric (CUNY)
Title: Horizontal foliation of integrable holomorphic quadratic differentials on infinite Reimann surfaces
Abstract: Let $X$ be an infinite Riemann surface with the covering group of the first kind. We prove that the Brownian motion on $X$ is recurrent iff a.e. horizontal leaf of every integrable holomorphic quadratic differential on $X$ is recurrent. When $X$ is such, we prove that the holomorphic quadratic differentials with single horizontal cylinders (the Jenkins-Strebel differentials) are dense among all integrable holomorphic quadratic differentials in the L^1-norm. We also extend Kerckhoff’s formula for the Teichmuller distance in terms of the extremal lengths of simple curves for such Riemann surfaces.
October 10: No seminar. (classes follow Monday schedule)
October 17: No seminar.
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October 24: Julien Paupert (Arizona State University)
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October 31:
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Novermber 7:
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November 14:
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Novermber 21:
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November 28: Blanca Marmolejo (Madrid)
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December 5: (Last seminar of the semester)
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Related seminars:
History of the hyperbolic geometry seminar