Fall 2020

Speaker: Ian Montague
Title: Curved Type A-infinity Modules and a Refinement of Bordered Sutured Floer Homology
Abstract: In this talk, I will introduce a refinement of Zarev's bordered sutured Floer homology analogous to Alishahi-Eftekhary's refinement of sutured Floer homology. Along the way, I will introduce some of the relevant Heegaard-Floer constructions, as well as some of the interesting algebraic objects which appear in the theory.

Speaker: Zihao Liu
Title: Topological Entropy and the First Homology Group
Abstract: The topological entropy h(f) of a map f: M \rightarrow M with M a compact manifold is a non-negative real number measuring how much f mixes up the space M. There is a general conjecture called Entropy Conjecture relating h(f) to rf_{*}, which is the spectral radius of the linear map induced by f on the total homology of M. The idea is that h(f) should be bounded below by log rf_{*}, i.e. f_{*} must capture some but not necessarily all of the mixing f does. In fact, the entropy conjecture is true for some special cases, but it is false in general. But if M is a compact differential manifold without boundary, then this conjecture holds for the first homology group.

Speaker: Gary Dunkerley
Title: Topological Quantum Field Theory and the Jones Polynomial
Abstract: The Jones polynomial is a powerful link invariant that is capable of distinguishing links from their mirror images. In the '80s, Edward Witten answered a question posed by Michael Atiyah: "Does the Jones polynomial have a physical meaning in the framework of topological quantum field theory?" Witten's work provides an interesting example of a broader pattern of connections between mathematical physics and the theory of smooth manifolds, one which has commanded significant attention over the last half century.