Math Seminar next week (21 July)

[math]

MATHEMATICS SEMINARS 2009

Tuesday, 21 July at 14:15

"Multipermutation solutions of the Yang-Baxter equation"

Professor Tatiana Gateva-Ivanova
(IMI, Bulgarian Academy of Sciences & AUBG)

Abstract: It is well-known that certain matrix solutions of the braid or
Yang-Baxter
equations lead to braided categories, knot invariants, quantum groups and
other important constructions. However, these equations are also very
interesting at the level of set maps $r:X\times X\to X\times X,$ where X
is a set and r is a bijection, a line of study proposed by Drinfeld.
Solutions extend linearly to very special linear solutions but also lead
to a great deal of combinatorics, and to algebras with very nice algebraic
and homological properties including those relating to  Artin-Schelter
regularity, Koszulity, being a PBW Noetherian domain,   and the existence
of noncommutative Groebner bases.

In this talk I will examine solutions  mainly from the point of view of
finite permutation groups: a solution gives rise to a map from X to the
symmetric group $Sym(X)$ on X satisfying certain conditions.

Our results include many new constructions based on strong twisted union
and wreath product, with an investigation of retracts and the
multipermutation level and the solvable length of the groups defined by
the solutions; and new results about decompositions and factorisations of
the groups defined by invariant subsets of the solution.
This talk is based on a joint work with Peter Cameron.

Venue: ICTP, Leonardo Building, Seminar Room