Math Seminar at ICTP - Monday, 9 November, at 16:00

[Math Group]

M A T H E M A T I C S   S E M I N A R S   2015

Monday, 9 November, at 16:00 hrs.

Anton Mellit (SISSA/ICTP)

A proof of the shuffle conjecture

16:00 - 16:50    Part I - Basic introduction

16:50 - 17:00    Coffee break

17:00 - 17:50    Part II - Technical discussion

Abstract: The shuffle conjecture gives a combinatorial interpretation of 
certain generating functions arising from the study of the action of the 
permutation group S_n on the algebra of polynomials in 2n variables x_1, 
y_1,..., x_n, y_n. The combinatorial side is given in terms of certain 
objects called parking functions, and the generating functions that 
arise there can be thought of as generalizations of Catalan numbers. The 
conjecture was formulated by Haglund and his collaborators in 2005, and 
since then attracted a lot of interest of algebraic combinatorists. 
During Erik Carlsson's stay at ICTP last year we were able to prove the 
conjecture, and that's what the talk will be about. First 50 minutes are 
intended for a general audience, I will talk about symmetric functions 
and demonstrate some important general tools for dealing with the 
generating functions of the kind we encountered. After a short break I 
will continue with more details on our proof.

Venue:  Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first 
floor)

-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building, room 106
Strada Costiera no. 11
34151 Trieste, Italy

Tel. no.: +39-040-2240455
math at ictp.it
http://math.ictp.it