*For this special year of the hyperbolic geometry seminar, please note the new location (Hunter College Room 921 Hunter East) and time (Wednesdays 3:30pm-5:30pm*
October 1st: Ara Basmajian (CUNY Graduate Center and Hunter College)
Title: A crash course on hyperbolic surfaces
October 8th: Ara Basmajian (CUNY Graduate Center and Hunter College)
Title: A crash course on hyperbolic surfaces (continued)
October 15th: Athanase Papadopoulos (Hunter College)
Title: On Funk geometry
Abstract: The Funk metric is a metric associated to a convex subset of Euclidean space. It is a non-symmetric version of the Hilbert metric, which in turn is a generalization of the hyperbolic metric. I will survey some classical and recent results on the Funk metric and formulate several questions.
October 22nd: Athanase Papadopoulos (Hunter College)
Title: Hilbert's fourth problem
Abstract: I will give a survey on Hilbert's Fourth problem from his collection of 23 problems he gave at the occasion of the 1900 Paris ICM. The problem asks for metrics on subsets of Euclidean space for which the Euclidean straight lines are geodesics.The Funk and the Hilbert geometries are examples of such metrics. I will survey several versions of this problem and the various solutions that have been given.
October 29th: Athanase Papadopoulos (Hunter College)
Title: Some classical theorems of spherical geometry and their hyperbolic analogues
Abstract: I will survey some theorems of spherical geometry, due to Euler and to others, and their analogues in hyperbolic geometry. I will also talk about the analogues of the Funk and Hilbert metrics in the non-Euclidean setting (spherical and hyperbolic).
November 5th: Athanase Papadopoulos (Hunter College)
Title: Spherical hyperbolic trigonometry
Abstract: The trigonometric formulae give relations between angles and sides of triangles. They are at the base of any geometry. I will show how the trigonometric formulae of spherical and hyperbolic geometry are related to each other and how they can be derived in a unified way.
November 12th: Christopher Arettines (CUNY Graduate Center)
Title: Filing curves on hyperbolic surfaces
Abstract: A curve on a surface is said to be filling if the complement is a disjoint union of topological disks or once punctured disks. These curves have interesting combinatorial and geometric properties which I will discuss.
November 19th: Christopher Arettines (CUNY Graduate Center)
Title: Angles of intersection on the punctured torus
Abstract: I will discuss how the angles of intersection formed by two special geodesics on the punctured torus can be used to determine the hyperbolic metric on the surface. I will not assume much knowledge, and build up the proof using the basics of hyperbolic geometry.
November 5th: Athanase Papadopoulos (Hunter College)
Title: The work of Maryam Mirzakhani
Abstract: I will present some the work of Maryam Mirzakhani and explain how it fits into a program started by Riemann.
Diversity and Inclusion at the GC