Abstract:
Lorentzian polynomials have recently garnered great interest in combinatorics and have proved to be a useful tool in attacking problems ranging from matroids to knot theory. In particular, they provide a bridge between the log-concavity of a polynomial as a function and the discrete log-concavity of its coefficients. In this talk, we will examine various efforts to generalize the theory of Lorentzian polynomials to delta matroids, which are a generalization of matroids naturally arising from areas as wide-ranging as matchings, principal minors, and ribbon graphs. We will first explore the motivation for this work, including an application for sampling from the bases of a delta matroid. Then, we will look at several ways one might try to generalize Lorentzianity to the delta matroid setting and examine where each falls short.
Note: Please note the special location, Smith 205. There will be no pre-seminar. The main talk starts at 4:10.
Join Zoom Meeting: https://washington.zoom.us/j/
Meeting ID: 915 4733 5974