A brief introduction to coinvariant algebras

Josh Swanson

We’ll start by examining Hilbert’s famous 1890 result which settled the “first problem of invariant theory” by introducing the coinvariant ideal and what is now called Hilbert’s Basis Theorem. Next, we’ll examine some of the many beautiful and intertwined combinatorial, algebraic, representation-theoretic, topological, and geometric properties of the coinvariant algebra of the symmetric group. Time permitting, we’ll mention some exciting recent work on diagonal and super diagonal coinvariants of pseudo-reflection groups.