Speaker: Jake Rasmussen (Robert and Ann Canary Professor, UIUC)
Title: From Alexander to Floer
Abstract: Given two knots in S^3, how can one distinguish them? One of the first useful invariants for doing so was defined 100 years ago by JW Alexander. ThisAlexander polynomial turns out to be related to a variety of interesting geometric questions we can ask about the knot, such as the minimal genus of a surface bounding it or whether the knot complement fibres over the circle.
I'll discuss the Alexander polynomial and some modern generalizations of it which are defined using Floer homology.
The talk will be followed at 5pm by a reception in Bevier Commons. Please join us at this reception to welcome our new Canary Professor and to inaugurate this year’s Colloquium series.