Alexander Wilson

The field of representation theory takes the philosophy that the best way to understand algebraic structures lies in the way they act on other mathematical objects like vector spaces. When we have such an action, we can think of it as representing an algebraic structure as the symmetries of the object. In my day-to-day work, you'll usually find me trying to decompose a representation into smaller, irreducible pieces and describing the multiplicities of these pieces as the enumeration of some set of combinatorial gadgets like graphs or tableaux. I primarily focus on representations of the symmetric group and simple Lie algebras.