Yibo Gao and Daoji Huang

Course Description

Algebraic combinatorics is a research area that studies the interplay between combinatorics and algebra, including representation theory, Lie theory and algebraic geometry. On the one hand, many abstract algebraic structures can be more conveniently described via combinatorics. On the other hand, combinatorial problems can be solved elegantly by algebraic techniques.

In this course, we will focus on the theory of symmetric functions and their generalizations. Along the way, we will explore the rich and fascinating combinatorics of Catalan objects, partitions, Young tableaux, permutations, Bruhat orders, pipe dreams, etc. Time permitting, more advanced topics including quasisymmetric functions and Schubert polynomials will be covered.