Augmented branching rules for symmetric groups in characteristic two

Key tools in the representation theory of the symmetric group S_n are the so-called branching rules. These combinatorial rules describe simple factors of S_n-representations upon restriction down to the subgroup S_n-1, or upon induction up to S_n+1. In the classical (semisimple) characteristic zero setting, branching is well understood and governed by elegant box removal/addition operations on Young diagrams. In the thornier (non-semisimple) characteristic two setting, Kleshchev established combinatorial rules which provide partial branching information. In this talk I will describe the modern approach to symmetric group representation theory via the larger and richer world of diagrammatic KLR algebras. These algebras act as a sort of categorical bridge between symmetric groups and quantum groups, and I will describe how we can use this connection to investigate a new augmented collection of branching rules for symmetric groups in characteristic two.