CUNY Graduate Center
365 Fifth Avenue, New York, NY 10016
Room: 4214-03 (Thesis room)
Tuesdays 3:00pm - 4:00pm
Ara Basmajian (CUNY, Graduate Center and Hunter College)
Email: abasmajian@gc.cuny.edu
Nick Vlamis (CUNY, Queens College)
Email: nicholas.vlamis@qc.cuny.edu
***Due the COVID-19 pandemic, the hyperbolic geometry will be cancelled for the rest of the Spring 2020 semester starting with the March 17 seminar.
Title: Tubular neighborhoods in complex hyperbolic manifolds
Abstract: We will prove that an embedded totally geodesic complex surface in a complex hyperbolic 2-manifold has a tubular neighborhood whose size depends only on its area.
Title: Quasisymmetric Koebe Uniformization
Abstract: Let X be a metric space that is homeomorphic to a planar domain. We provide some necessary and some sufficient conditions for X to be quasisymmetric to a domain in the complex plane \mathbb{C}, whose every complementary component is either a round disk or a point.
Title: Knots and links as periods in 3D fluid motion
Title: Dilogarithm identities for solutions to Pell's equation in terms of continued fraction convergents
Abstract: We describe a new connection between the dilogarithm function and solutions to Pell's equation $x^2-ny^2 = \pm 1$. For each solution $x,y$ to Pell's equation we obtain a dilogarithm identity whose terms are given by the continued fraction expansion of the associated unit $x+y\sqrt{n} \in \Z[\sqrt{n}]$.
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Title: On the L^2 geometry of the space of hyperbolic metrics
Abstract We give a survey of the L^2 geometry of the space of hyperbolic metrics. It includes the Weil-Petersson geometry of Teichmueller spaces as a Riemannian sub-manifold. The differential geometric viewpoint is complementary to the complex analytic method initiated by Ahlfors and Weil, but we will see that it has certain advantages in describing the geometric properties of the deformation theory of Riemann surfaces.
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