Permutations, partitions, and posets: a taste of combinatorial representation theory
Time and place
12:45–1:45 PM on Thursday, June 16th, 2022; MR-1
Zajj Daugherty (CCNY)
Abstract
Representation theory is the study of abstract algebraic structures (like groups and rings) by way of representing them as sets of linear maps that follow the same addition and multiplication rules. By understanding the representations of a group, we can see concrete snapshots of that group's structure, and isolate behavior one piece at a time. This approach has powerful applications throughout mathematics, physics, engineering, social science, and elsewhere. Combinatorial representation theory uses discrete objects (like partitions, tableaux, graphs, etc.) to encode and track representation theoretic data. We'll briefly explore some of the many ways the quintessential example--the symmetric group--evokes this interplay between combinatorics and representations.
