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!

I will describe a lovely, classical theorem of Graham and Pollak about a network switching problem. This helps motivate a new result about distance matrices for trees. Its applications include proofs of two recent conjectures about inequalities involving the number of independent sets of a matroid. This is joint work with Federico Ardila, Chris Eur, June Huh and Botong Wang.