Seminar on mirror symmetry and representation theory

Tuesday, March 14, 5:00-6:30, MIT, room 2-132.

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

by Joel Kamnitzer (MIT).

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)