Sylvie Corteel (CNRS, LIAFA, Université Denis Diderot - Paris 7, Miller Institue at UC Berkeley):

Title: Lecture Hall Tableaux

Abstract: The lecture hall partitions were introduced by Bousquet-Mélou and Eriksson in 1997 by showing that they are the inversion vectors of elements of the parabolic quotient $\tilde{C}_n/C_n$. Since 1997, a lot of beautiful combinatorial techniques were developed to study these objects and their generalisations. These use basic hypergeometric series, geometric combinatorics, real rooted polynomials... Some of those results can be found in the survey paper by C. D. Savage "The Mathematics of lecture hall partitions". Here we take a different approach and show that these objects are also multivariate moments of the Little $q$-Jacobi polynomials. The multivariate moments were introduced by Williams
and me in the context of asymmetric exclusion processes. The benefit of this new approach is that we define a tableau analogue of lecture hall partitions and we show that their generating function is a beautifulproduct. This uses a mix of orthogonal polynomials techniques, non intersecting lattice paths and $q$-Selberg integral. This is joint work with Jang Soo Kim (SKKU).

The talk will not require any prerequisite on the subjects.

Allen Knutson (Cornell): 

Title: TBA

Abstract: TBA

Franco Saliola (UQAM):

Title: A Murnaghan-Nakayama Rule for Quantum Cohomology of the Flag Manifold

Abstract: I will present a general rule for multiplying a quantum Schubert polynomial by a quantum power sum polynomial. This is achieved by relating the structure constants for the multiplication of a quantum Schubert polynomial by a hook quantum Schur polynomial with the structure constants for the (classical) multiplication of a Schubert polynomial by a hook Schur polynomial. This is joint work with C Benedetti, N Bergeron, L Colmenarejo and F Sottile. 

Monica Vazirani (UC Davis): 

Title: TBA

Abstract: TBA