Elisenda Grigsby, Columbia

TITLE: On knot homology theories

ABSTRACT: Understanding knots (smoothly-imbedded circles in 3-manifolds, considered up to isotopy) is essential for understanding 3- and 4-dimensional manifolds.  I will discuss two recently-developed tools for studying knots, both inspired by ideas in physics: Khovanov homology and Heegaard Floer homology. In the less than ten years since their introduction, they have generated a flurry of activity and a stunning array of applications. There are also intriguing connections between the two theories that have yet to be fully understood.