Algebraic Geometry Seminar

A recent series of results prove finiteness results for degrees of equations or syzygies for families of algebraic varieties by packaging them into a single algebraic structure and proving a noetherian result. I will survey some of this work, mostly related to Segre products of projective spaces and their secant varieties. Twisted commutative algebras appear as auxiliary structures and proving analogs of Hilbert's basis theorem for them has proven to be challenging. I will explain some of my recent work in this direction.