Matroids, polymatroids and submodular functions: algebra or optimization?

Abstract: Matroids, polymatroids and submodular functions are beautiful objects that have appeared in many areas of mathematics including algebra, geometry, topology and optimization. Consequently, they have been studied from multiple points of view. This oftentimes has the consequence that the same results are proven from different points of view and by very different communities. A notable example being their study in optimization and algebraic combinatorics. The goal of this talk is to tell this story, show how a small mixture of ideas from different communities lead to powerful algebraic tools, and speculate a little a bit about the opposite direction.

Posted on Nov 30, 2020 in ACGO, Seminars