September 21st: Ara Basmajian (CUNY Graduate Center and Hunter College)
Title: Orthogonal spectrum
September 28th: Ara Basmajian (CUNY Graduate Center and Hunter College)
Title: Orthogonal spectrum (part 2)
October 5th: No meeting
October 12th: Karan Puri (CUNY Queensborough Community College)
Title: Generating the Möbius groups with involution conjugacy classes
October 19th: Karan Puri (CUNY Queensborough Community College)
Title: Generating the Möbius groups with involution conjugacy classes (continued)
October 26th: Ege Fujikawa (Chiba University)
Title: An introduction to asymptotic Teichmüller space
November 2nd: Viveka Erlandsson (CUNY Graduate Center)
Title: Hyperbolic 3-manifolds with nonintersecting closed geodesics
Abstract: I will present a paper ``Hyperbolic 3-Manifolds with Non0intersecting Closed Geodesics'' by Ara Basmajian and Scott Wolpert.
A hyperbolic 3-manifold has the spd-property if all its closed geodesics are simple and pairwise disjoint. It is shown that for a manifold that admits a geometrically finite hyperbolic structure, either the generic hyperbolic structure has the spd-property or no hyperbolic structure has it, and examples of each case are given. In particular, the generic structure on the interior of a handlebody, or surface cross an interval, possesses the spd-property.
November 9th: David Futer (Temple University)
Title: Complex hyperbolic quasi-Fuchsian space
Abstract: Given a surface of genus g>1, and a polygon with p sides, does there exist a tiling of this surface by right angled p-gons. If yes, how ``nice'' can we make this tiling? For example, do the edges of the tiling join up into embedded, separating geodesics on the surface.
These questions about surfaces are fun to ponder, and can be answered with fairly elementary means. What's surprising is that the answers to the questions lead quite naturally to information about the symmetry group of much more complicated ``buildings'' that are constructed out of right angled p-gons.
November 16th: Youngju Kim (Korea Institute for Advanced Study)
Title: Complex hyperbolic quasi-Fuchsian space
November 23rd: Viveka Erlandsson (CUNY Graduate Center)
Title: Hyperbolic 3-manifolds with nonintersecting closed geodesics (continued)
November 30th: Ozgur Evren (CUNY Graduate Center)
Title: Further results on the length spectrum metric
Abstract: In this talk, we will discuss some results from a 2008 paper by Lixin Liu, Zongliang Sun, and Hanbai Wei concerning the Length Spectrum Metric dL and Thurston's asymmetric metrics dPi on Teichmüller space T(X). Namely, we will show that one can always find two sequences {σn} and {τn} such that dL(σn, τn) → 0, dPi(σn, τn) → 0 while dT(σn, τn) → ∞ where dT denotes the Teichmüller metric. As an application of this theorem, we will prove that dL and dPi do not necessarily define the same topology as dT for surfaces of infinite topological type, a result originally due to Shiga.
Decmber 7th: Ara Basmajian (CUNY Graduate Center and Hunter College)
Title: Orthogonal spectrum (part 3)
Diversity and Inclusion at the GC