DMS Algebra Seminar

Speaker: Luke Oeding (Auburn University)

Title: What we know and don’t about the invariant ring for 5 qubits

Abstract: Invariant rings for spaces of tensors are particularly nice: they are finitely generated, and Cohen-Macaulay, and in the tame cases (the set of orbits depending on finitely many parameters) they are even polynomial rings. We can compute their Hilbert series via computations with finite groups. But what if we want to do computations with invariants? Schur-Weyl duality and Young symmetrizers provide a way to access and evaluate these functions at least in low degrees. The first case of qubits with wild orbit type is with 5 qubits. I will discuss our attempt to compute a set of primary invariants in this case, and I will explain why this result is almost surely correct, yet we cannot prove it.