Special Year Seminar

Tropical ideals are combinatorial objects that abstract the behavior of the collections of subsets of lattice points that arise as the supports of all polynomials in an ideal. Their structure is governed by a sequence of ‘compatible’ matroids and...

In 2008, looking to bound the face vectors of tropical linear spaces, Speyer introduced the g-invariant of a matroid, defined in terms of exterior powers of tautological bundles on Grassmannians. He proved its coefficients nonnegative for matroids...

Equivariant cohomology was introduced in the 1960s by Borel, and has been studied by many mathematicians since that time.  The talks will be an introduction to some of this work.  We will focus on torus-equivariant cohomology (as well as Borel-Moore...

Equivariant cohomology was introduced in the 1960s by Borel, and has been studied by many mathematicians since that time.  The talks will be an introduction to some of this work.  We will focus on torus-equivariant cohomology (as well as Borel-Moore...

The construction by Mikhalkin of a non-planar tropical cubic curve in R^3 of genus 1 marked a significant breakthrough in the study of combinatorial tropical varieties. It was the first known example of a non-realizable tropical variety, with the...

The conjecture in combinatorics that has received perhaps the most attention over the last 50 years is McMullen's g-conjecture. It provides a complete characterisation of the number of i-dimensional faces in a triangulation of an (d−1)-dimensional...

In a landmark paper in 1992, Stanley developed the foundations of what is now known as the Kazhdan--Lusztig--Stanley (KLS) theory. To each kernel in a graded poset, he associates special functions called KLS polynomials. This unifies and puts a...

We heard last week in Daoji's talk about positroid varieties, which are subvarieties in the Grassmannian defined by cyclic rank conditions, and which are related to Schubert varieties. In this talk, we will provide a criterion for whether positroid...

A valuation is a finitely additive measure on the class of all convex compact subsets of Rn. Over the past two decades, a number of structures has been discovered on the space of translation invariant smooth valuations. Recently, these findings...

Influential work of Hodge from the 1940s led the way in using Gröbner bases to combinatorially study the Grassmannian. We follow Hodge's approach to investigate certain subvarieties of the Grassmannian, called positroid varieties. Positroid...