Date: Tuesday Feb 3rd & 10th 2015

Speaker: Seungwon Kim

Title: Link diagrams with Turaev genus one

Abstract : Every link diagram is cellularly embedded on its Turaev surfaces and is alternating on it. However, not every cellularly embedded alternating diagram on a surface comes from Turaev's construction. I will talk about a necessary condition for such a diagram to arise from Turaev's construction, and use it to classify link diagrams with Turaev genus one.

Date: Tuesday Feb 24th, March 3rd & 17th 2015

Speaker: Zach McGuirk

Title: Expansion in graphs and Expansion Phenomena

Abstract: This talk is the first of a series of planned lectures on Expansion Phenomena. In this talk the background material for an understanding of the Bourgain-Gamburd Expansion Machine will be presented. In particular, the basic graph theory required will be covered and the setting necessary to fire up the machine will be constructed with a statement of the theorem at the heart of this discussion coming in at the very end.

Date: Tuesday March 10th 2015

Speaker: Joe Quinn

Title: Canonical decompositions for cusped hyperbolic manifolds

Abstract: We will discuss canonical decompositions for cuspsed hyperbolic manifolds described in Epstein-Penner's famous paper "Euclidean decompositions of noncompact hyperbolic manifolds".

Date: Tuesday April 14th & 21st 2015

Speaker: Ivan Levcovitz

Title: Geometry in Coxeter Groups

Abstract: This talk will discuss the geometry of general Coxeter groups. I will define these groups, prove some of their basic geometric and combinatorial properties, and examine geometric spaces these groups act on. Many examples will be given.