MAAGC 2018 ABSTRACTS
Sylvie Corteel (CNRS, LIAFA, Université Denis Diderot - Paris 7, Miller Institue at UC Berkeley):
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 Allen Knutson (Cornell): Title: TBAAbstract: 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: TBAAbstract: TBA |