Nikola Kuzmanovski: A structural property of generic initial ideals

Abstract: For over a century mathematicians have studied how to transfer information between a homogeneous ideal and its initial ideal. In this talk I will take up this topic in the context of regular sequences. I will present an asymptotic structural property of generic initial ideals. This single phenomenon yields results on Hilbert functions, persistence, hyperplane restriction, graded Betti numbers, combinatorial shadow minimization, and Lefschetz properties.