Representations of Sl(2,C) in combinatorics

Student Algebraic Geometry Seminar
Friday, January 29, 2021 - 9:00am for 1 hour (actually 50 minutes)
Microsoft Teams
Trevor Gunn – Georgia Tech
Trevor Gunn

There are two purposes of this talk: 1. to give an example of representation theory in algebraic combinatorics and 2. to explain some of the early work on unimodal/symmetric sequences in combinatorics related to recent work on Hodge theory in combinatorics. We will investigate the structure of graded vector spaces $\bigoplus V_j$ with two "shifting" operators $V_j \to V_{j+1}$ and $V_j → V_{j-1}$. We will see that this leads to a very rich theory of unimodal and symmetric sequences with several interesting connections (e.g. the Edge-Reconstruction Conjecture and Hard Lefschetz). The majority of this talk should be accessible to anyone with a solid knowledge of linear algebra.