Colloquium - Ying Anna Pun

Date: January 28, 2022

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Ying Anna Pun, University of Virginia

Description:
Title: Symmetric functions -- a gem in algebraic combinatorics
Abstract: Algebraic combinatorics is a subject that interprets algebraic objects combinatorically and combinatorial objects algebraically, thereby obtaining deep connections between the two areas. The study of polynomial rings is one of the important topics in algebraic combinatorics, as the associated combinatorial tools provide profound connections with partitions of integers and the representation theory of the symmetric group, the general linear group, Lie algebra, Hecke algebras, elliptic Hall algebra, shuffle algebra and other important algebras. It also gives fruitful information on objects in algebraic geometry such as the multiplicative structure of the cohomology ring of the Grassmannian. In this talk, I will introduce the ring of symmetric functions and discuss some important bases and their associated combinatorial objects. I will then discuss some conjectures and theorems in algebraic combinatorics that are inspired by the Macdonald positivity conjecture and end with a brief introduction to Catalanimals, an exciting powerful tool to prove these theorems.