Austin Roberts: Developments in the theory of Macdonald Polynomials

Current Topics Seminar

Speaker	Austin Roberts
Title	Developments in the theory of Macdonald Polynomials
Date	March 10 2:30PM PDL C-36

Macdonald Polynomials were a conjectured basis for the symmetric functions with properties relating them to representation theory and other well known polynomial families. In 2005, Haglund, Haiman, and Loehr gave an explicit combinatorial description of Macdonald polynomials, setting the stage for a flurry of future advances. Their paper uses fillings of partition diagrams and so immediately opens the door to many connections within algebraic combinatorics. In this talk, we will focus on describing the combinatorial representation of Macdonald Polynomials as well some recent developments on related problems. The talk will be aimed at a wide audience, and no prior knowledge will be assumed.