Algebra & Geometry Seminar

Speaker: Jason McCullough (ISU)
Title: Unimodality
Abstract: A sequence of positive numbers a_0, a_1,…,a_n is unimodal if a_0 \le a_1 \le … \le a_t \ge … \ge a_n for some t. There are many combinatorial problems that come from considering unimodal sequences. I will survey unimodality and stronger notions like log-concavity, ultra log-concavity, gamma-positivity, and real rootedness and connections with Lefschetz properties of graded algebras. This will be a low-level talk with very few prerequisites.