# Cascade Topology Seminar, Spring 2015, abstracts

Speaker: Tali Pinsky

Title: On the volumes of complements of geodesics on Surfaces.

Abstract: TBA

Speaker: Allison Heinrich

Title: Pseudoknots and their invariants.

Abstract: TBA

Speaker: David Ayala

Title: Some abstract applications of factorization homology.

Abstract: TBA

Speaker: Balazs Strenner

Title: Pseudo-Anosov mapping classes arising from Penner’s construction.

Abstract: There are many constructions of pseudo-Anosov elements of mapping class groups of surfaces. Some of them are known to generate all pseudo-Anosov mapping classes, others are known not to. In 1988, Penner gave a very general construction of pseudo-Anosov mapping classes, and he conjectured that all pseudo-Anosov mapping classes arise this way up to finite power. This conjecture was known to be true on some simple surfaces, including the torus, but has otherwise remained open. In this talk I prove that the conjecture is false for most surfaces. (This  is joint work with Hyunshik Shin.)

Speaker: Chuck Livingston

Title: A survey of recent work on knot concordance.

Abstract: TBA

Speaker: Maxime Bergeron

Title: The topology of representation varieties

Abstract: Let H be a finitely generated group and let G be a complex reductive linear algebraic group (e.g. a special linear group). The representation space Hom(H,G), carved out of a finite product of copies of G by the relations of H, has many interesting topological features. From the point of view of algebraic topology, these features are easier to understand for the compact subspace Hom(H,K) of Hom(H,G) where K is a maximal compact subgroup of G (e.g. a special unitary group). Unfortunately, the topological spaces Hom(H,G) and Hom(H,K) usually have very little to do with each other; for instance, some of the components of Hom(H,G) may not even intersect Hom(H,K). Accordingly, I will discuss exceptional classes of groups H for which Hom(H,G) and Hom(H,K) happen to be homotopy equivalent, thereby allowing one to obtain otherwise inaccessible topological invariants.