Title: Quotients of lattice path matroids


Abstract: In this talk we will focus \;on a particular class of matroids called Lattice Path Matroids (LPMs). We will determine when a collection M_1,...,M_k of LPMs are a flag matroid, using their combinatorics. Part of our work will show that the polytope associated to such a flag can be thought as an interval in the Bruhat order, and thus provides a partial understanding of flags of LPMs from a polytopal point of view.

We will not assume previous knowledge on quotients. This is joint work with Kolja Knauer.


Where: Seminar Room @ Villa and Zoom:
https://sfsu.zoom.us/j/82165524617?pwd=Vkwzd1RhaEpqcFVncTRaWmNpUjBCQT09

Meeting ID: 821 6552 4617
Passcode: 180147

Title: Toric Newton-Okounkov functions and polytopes


Abstract: We initiate a combinatorial study of Newton-Okounkov functions on toric varieties with an eye on the rationality of asymptotic invariants of line bundles. In the course of our efforts we identify a combinatorial condition which ensures a controlled behavior of the appropriate Newton-Okounkov function on a toric surface. \;
Our approach yields the rationality of many Seshadri constants that have not been settled before. This is joint work with Christian Haase and Alex Küronya. In the upcoming talk I will explain the setup from a discrete geometer's point of view and how polyhedral methods can be used to study the above problem.



Where: Seminar Room @ Villa and Zoom:
https://sfsu.zoom.us/j/82165524617?pwd=Vkwzd1RhaEpqcFVncTRaWmNpUjBCQT09

Meeting ID: 821 6552 4617
Passcode: 180147