Forthcoming Mathematics Seminar at ICTP

[Mabilo Koutou]

  M A T H E M A T I C S   S E M I N A R S   2007


Wednesday, 9 May, at 14.30 hrs.
Professor Jozef H. Przytycki

(George Washington University and UMD)

"Introduction to Khovanov homology of knots via Hochschild homology  
of algebras"

Abstract:

We offer a gentle introduction to the theory of Khovanov homology of  
links in R^3. We start from link diagrams and Reidemeister moves,  
then we define Kauffman bracket invariant (a framed version of the  
Jones polynomial) and illustrate its basic property. Khovanov  
homology categorifies the Jones polynomial; we show how Hochschild  
homology of algebras (truncated polynomials in this case) can be used  
to introduce Khovanov homology. The deep theory of Hochschild  
homology and related Connes cyclic homology illuminates the  
foundation of Khovanov theory.


Venue: Seminar room (ICTP Main Building, first floor)