Tutte Colloquium - François Bergeron

Tuesday, March 10, 2020 8:42 am - 8:42 am EDT (GMT -04:00)

Title: Rectangular Catalan Algebraic Combinatorics

Speaker François Bergeron
Affiliation LACIM - Université du Québec à Montréal
Room MC 5501


The enumeration of Dyck-like lattice paths in a m x n rectangle has a long and fruitful history culminating in Bizley-Grossman’s formula (1954). We will discuss how it is natural to extend this formula to weighted enumeration, with parameters accounting for such statistics as area; and to consider parking-function analogs. In fact, we will show how all these enumeration problems maybe be jointly solved using a generating function approach involving symmetric functions. If time allows, we will also explain how all this may be synthesized via an operator realization of the elliptic Hall algebra (introduced by Burban-Vasserot-Schifmann); as well as discuss some aspects of interesting connections with many areas including: Algebraic Combinatorics (rectangular Catalan combinatorics), Symmetric Functions (compositional shuffle conjecture/theorem, nabla operator), Knot Theory (Khovanov-Rozansky homology of (m,n)-torus knots), and Theoretical Physics (boson-fermion supersymmetry).