Talk by Dr. Paul Wedrich (Mathematics, Australian National University)

1/31/2019  Wilson Hall 1-144  4:10-5:00pm

Abstract: Link homology theories are powerful generalizations of knot polynomials. Besides being better at distinguishing links, these theories are often functorial under link cobordisms and contain additional topological information. I will start by introducing Khovanov homology, a paradigmatic example of a link homology theory, and explain how it fits into the family of colored gl(N) link homologies. I will then survey what is known about relationships between members of this family of invariants, about the topological information they detect, and why they appear in many parts of mathematics. I will finish by outlining the next steps towards extending these theories to invariants of 3- and 4-manifolds.