Bijective Combinatorics of Young Tableaux

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

In the past few years there has been a growing number of connections between enumerative algebraic geometry, in particularly Gromov-Witten theory, and the algebraic combinatorics, in particular Young tableaux identities. The proposer intend to pursue the study of combinatorial bijections related to these identities. In particular, he intends to investigate multi-weighted analogues of certain classical combinatorial identities which also arise naturally from the representation theory of the symmetric group. He also intends to pursue both enumerative, algebraic and probabilistic applications of the discrete random processes for generation of weighted Young tableaux. Young tableaux are basic combinatorial structure which were introduced over a hundred years ago in connection with studies of a large class of spaces with symmetries. Over the years, Young tableaux have been further studied in connection with other fields of studies, such as statistical physics, discrete probability, and more recently, algebraic geometry and field theory. The reviewer intends to pursue the combinatorial aspects of the latter connections, with the intension of developing new tools, which in turn will lead to new results in both fields.