August 29th: Youngju Kim (Konkuk University)
Title: Complex hyperbolic p_Schottky groups
Abstract: In this talk, we generalize a Schottky group construction to complex hyperbolic space. In particular, we construct a fundamental domain whose sides consist of disjoint non-asymptotic packs for the action of the Schottky group on complex hyperbolic space.
February 14th: No meeting (Scheduling conflict)
February 21st: No meeting (Scheduling conflict)
February 28th: Daniel Berlyne (CUNY Graduate Center)
Title: Hyperbolic ideal tetrahedra and volume
Abstract: We will compute the volume of an ideal tetrahedron and discuss its significance in relation to knot theory and Mostow rigidity.
March 7th: Daniel Berlyne (CUNY Graduate Center)
Title: Hyperbolic ideal tetrahedra and volume (continued)
March 14th: Meeting cancelled due to heavy snow
March 21st: Alice Kwon (CUNY Graduate Center)
Title: Ideal triangulations and gluing equations
Abstract: We will give examples of ideal triangulations for knot and link complements and describe Thurston's gluing equations.
March 28th: No meeting (Scheduling conflict)
April 4th: Ivan Levcovitz (CUNY Graduate Center)
Title: Divergence of CAT(0) cube complexes and right-angled Coxeter groups
Abstract: The divergence function of a metric space, a quasi-isometry invariant, roughly measures the rate that pairs of geodesic rays stray apart. We will present new results regarding divergence functions of CAT(0) cube complexes. Right-angled Coxeter groups, in particular, exhibit a rich spectrum of possible divergence functions, and we will give special focus to applications of our results to these groups. Applications to the theory of random right-angled Coxeter groups will also be briefly discussed.
April 11th: No meeting (Spring recess)
April 18th: No meeting (Spring recess)
April 25th: Nicholas Vlamis (University of Michigan)
Joint meeting with CUNY Geometry and Topology Seminar. Please note this meeting is in room 3212 at 4:15pm.
Title: Algebraic and topological properties of big mapping class groups
Abstract: There has been a recent surge in studying surfaces of infinite type, i.e., surfaces with infinitely-generated fundamental groups. In this talk, we will focus on their mapping class groups, often called big mapping class groups. In contrast to the finite-type case, there are many open questions regarding the basic algebraic and topological properties of big mapping class groups. I will discuss several such questions and provide some answers. In particular, I will focus on automorphisms of pure mapping class groups. This work is joint with Priyam Patel.
Link to CUNY Geometry and Topology Seminar: Geometry and Topology Seminar
May 2nd (Doubleheader): Rochy Flint (CUNY Graduate Center)
Joint meeting with CUNY Geometry and Topology Seminar
Title: Intercusp geodesics and cusp shapes of fully augmented links
Abstract: We study the geometry of fully augmented link complements in the 3-sphere by looking at their link diagrams. We extend the method introduced by Thistlethwaite and Tsvietkova to fully augmented links and define a system of algebraic equations in terms of parameters coming from edges and crossings of the link diagrams. Combining it with the work of Purcell, we show that the solutions to these algebraic equations are related to the cusp shapes of fully augmented link complements. As an application we use the cusp shapes to study the commensurability classes of fully augmented links
Link to CUNY Geometry and Topology Seminar: Geometry and Topology Seminar
Carolyn Abbott (University of Wisconsin-Madison)
Joint meeting with CUNY Geometry and Topology Seminar in Room 3212 at 4:15pm.
Title: Extending acylindrical actions
Abstract: Given a group G and a subgroup H, it is natural to ask when an action of H on a metric space can be extended to an action of G on a (possibly different) metric space. One might further ask when this extension preserves certain properties of the action of H, such as acylindricity of the action and hyperbolicity of the space. I will discuss when such an extension is possible for a certain class of subgroups of acylindrically hyperbolic groups. I will also give applications of this result to universal acylindrical actions.
Link to CUNY Geometry and Topology Seminar: Geometry and Topology Seminar
Diversity and Inclusion at the GC