Geometry Forum
Wednesday, April 15, 2009, 1:00pm, 047 Physics
Lenhard Ng (Duke University)
Categorification and Khovanov homology
Abstract:- About a decade ago, Mikhail Khovanov began a revolution in low-dimensional topology with his work on categorification (briefly stated, a strategy for upgrading sets and functions to categories and functors). One celebrated example of categorification in topology is Khovanov homology, a bigraded homology theory for knots whose Euler characteristic is the Jones polynomial. I will introduce Khovanov homology and describe some of its applications, such as a combinatorial/nonanalytic proof of the Milnor conjecture, previously proven using gauge theory. The subject is accessible enough not to require any real background, though spectral sequences may briefly appear at some point.
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