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Braid groups and their 2-representations

Presented by: 
Anthony Licata Australian National University
Tuesday 17th January 2017 - 14:30 to 15:30
INI Seminar Room 1
The main topic of this lecture series will be the Artin braid group B_n.  We study this group using two main tools:
1) linear 2-representations of B_n, and
2) annular Khovanov homology (see Eli Grigsby's lectures).
The first lecture will introduce the braid group, explain what it means for B_n to act on a category, and motivate the study of 2-representations of braid groups.
In later lectures, we will study a particular example of a (faithful) 2-representation of B_n - the categorified Burau representation - in detail, and explain how various structures of interest in the study of the braid group can be studied through the lens of this 2-representation.  Time permitting, we will discuss the relationship between linear 2-representations of B_n and geometric representation theory.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons