"Garnir modules, Hall-Littlewood polynomials, and the cohomology of

Springer fibers"

One classical construction of the irreducible representations of the symmetric group is as spaces of polynomials in n variables.  However, apparently no one has previously studied the ideal these polynomials generate.  I will describe the representation theory of these ideals.  It turns out that determining this representation theory involves not only algebra and combinatorics, but also algebraic geometry and topology.  This is joint work with Mark Haiman

"Symplectic and smooth four-manifolds via singular fibrations"

We will survey various results on the existence and uniqueness of maps with prescribed singularities on four-manifolds, along with certain classes of singular fibrations, by means of which the smooth type of the underlying manifold can be prescribed combinatorially.

"TBA"

"TBA"

"TBA"

Anne Schilling, UC Davis

Nicolas M Thiery, Université Paris Sud.

"Sorting monoids and algebras on Coxeter group"

Talk 1- General Audience Talk

The usual combinatorial model for the 0-Hecke algebra H_n(0) (in type A) is to consider the algebra (or monoid) generated by the bubble sort operators pi_1,...,pi_{n-1}, where pi_i acts on words of length n and sorts the letters in positions i and i+1. This construction generalizes naturally to any finite Coxeter groups.

By combining several variants of those operators (sorting, antisorting, affine) we construct several monoids and algebras.  Astonishingly, they are endowed with very rich structures which relate to the combinatorics of descents and of several partial orders (such as Bruhat and left-right weak orders). These structures can be explained by numerous connections with representation theory, and in particular with affine Hecke algebras, and symmetric functions.

Anne Schilling, UC Davis

Nicolas M Thiery, Université Paris Sud.

"Sorting monoids and algebras on Coxeter group"

Talk 2

The usual combinatorial model for the 0-Hecke algebra H_n(0) (in type A) is to consider the algebra (or monoid) generated by the bubble sort operators pi_1,...,pi_{n-1}, where pi_i acts on words of length n and sorts the letters in positions i and i+1. This construction generalizes naturally to any finite Coxeter groups.

By combining several variants of those operators (sorting, antisorting, affine) we construct several monoids and algebras.  Astonishingly, they are endowed with very rich structures which relate to the combinatorics of descents and of several partial orders (such as Bruhat and left-right weak orders). These structures can be explained by numerous connections with representation theory, and in particular with affine Hecke algebras, and symmetric functions.

"TBA"

Good Friday

University Holiday

"TBA"

"TBA"