Introduction: Topics of these seminars include differential equations (ODEs, PDEs, DDEs, FDEs, etc.), dynamical systems theory, and their applications (often in mathematical biology). To get the brain gears turning, each session will kick off with a fun trivia!

In this talk, we demonstrate a strong connection between log-concavity statements and sampling algorithms. In particular, we will present and discuss two general results (one log-concavity and one sampling) on the facets of certain simplicial complexes which generalize the set of chains in distributive or matroid lattices. With the time that remains, we will discuss how these two results can be derived from a single unified framework via Lorentzian polynomials on cones. Joint work with Kasper Lindberg and Shayan Oveis Gharan.