I will start by describing Khovanov's idea of "knot homology". The goal is to find bi- and tri-graded vector spaces whose graded Euler characteristics are classical polynomial knot invariants (like the Jones or HOMFLYPT polynomial). I will then explain how HOMFLYPT homology can be given a transparent construction using techniques from geometric representation theory. This provides at least one reason for people who work with braid groups, Hecke algebras and groups of Lie type to be interested in knot homology.
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After the seminar we will take the speaker to lunch.
See the Algebra Seminar web page for information about other seminars in the series.
James East jamese@maths.usyd.edu.au
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