Title: Khovanov Homology and its Torsion
Alexander Shumakovitch (George Washington University)

Abstract:
  Khovanov homology is a new approach to construction of knot (or link)
  invariants. Its idea is to replace a well-known knot invariant, say,
  the Jones polynomial, with a family of chain complexes, such that the
  coefficients of the original polynomial are the Euler characteristics
  of these complexes. Although the chain complexes themselves depend
  heavily on a diagram that represents the knot, the homology of these
  complexes depend on the isotopy class of the knot only.

  The ranks of the Khovanov homology groups have many remarkable
  properties. The goal of this talk is to show that their torsion is
  equally, if not more, interesting and fascinating. We will demonstrate
  certain relations between torsion and ranks of the Khovanov homology,
  prove that some of them are true for a certain class of knots, discuss
  various methods of computing the torsion and, finally, formulate
  several conjectures about it.

  This talk will be accessible to graduate and advanced undergraduate
  students.