Abstract

Matroids are a combinatorial abstraction of the notion of linear independence in a vector space. Since their introduction in the 1930s by Whitney and Nakasawa they have become part of the standard toolkit in various areas such as combinatorics, combinatorial optimisation, and computer science. In recent years there have been several ground breaking developments that have used techniques from algebraic geometry to prove deep theorems in matroid theory, and vice versa. A spectacular example of this is the recent proof, by Adiprasito, Huh, and Katz, of Rota-s log-concavity conjecture. The goal of this workshop is to build on these breakthroughs, and further develop the community at this interface between combinatorics and algebraic geometry. We aim to bring together a mix of experts who have already worked on these topics with specialists in neighbouring areas to develop the next steps in this exciting area.