Seminar on mirror symmetry and representation theory

Tuesday, March 21, 5:00-6:30, MIT, room 2-132.

Knot homology from symplectic geometry of slices after Seidel-Smith (continued)

by Joel Kamnitzer (MIT).

The talk is a continuation from 3/14. About a half of the topics mentioned in the following abstract have been explained in the first talk.

Abstract. We will discuss Seidel-Smith construction of knot homology using transverse slices to nilpotent orbits in sl_{n}. First we will give some theoretical motivation for choosing these orbits. Then we will explain the

construction of certain Lagrangians by vanishing cycles. Next we will describe an action of the braid group on the these slices by monodromy.

Finally we will see how these ingredients can be used to define knot homologies.

seminar contacts: Roman Bezrukavnikov (bezrukav@math.mit.edu); Rina Anno (rina@math.harvard.edu)