Special Year Seminar

I will present a (cohomological) Fourier-Mukai transform for tropical Abelian varieties and give some applications, including a (generalized) Poincaré formula (for non-degenerate line bundles on tropical Abelian varieties).

Based on joint work with...

In their recent paper, Giansiracusa and Manaker introduced a notion of tropical subrepresentations of linear representations by considering linear actions on tropical linear spaces. In particular, this framework naturally brings matroids into the...

The Khovanskii-Teissier inequality provides the fundamental log-concavity property of intersection numbers of divisors of algebraic varieties, extending the Alexandrov-Fenchel inequality of convex geometry. In this talk I will explain, and attempt...

For a complex elliptic curve E and a point p of order n on it, the images of the points pk=kp under the Weierstrass embedding of E into CP2 are collinear if and only if the sum of indices is divisible by n. We prove that for n at least 10 a...

The long-standing F-Conjecture asserts that there is a very simple description for the closed cone of effective curves on the moduli space M_{g,n}\bar of stable n-pointed curves of genus g as being determined by a finite collection of so-called F...

I will discuss various applications of a combinatorial model for the (torus equivariant) quantum K-theory of flag manifolds G/B, called the quantum alcove model. This is a uniform model for all Lie types, based on Weyl group combinatorics. It first...

I will show that any Schubert or Richardson variety R in a flag manifold G/P is equivariantly rigid and convex. Equivariantly rigid means that R is uniquely determined by its equivariant cohomology class, and convex means that R contains any torus...

In part 1, I will survey the history of total positivity, beginning in the 1930's with the introduction of totally positive matrices, which turn out to have surprising linear-algebraic and combinatorial properties. I will discuss some modern...

Configuration spaces of points in graphs are nonsmooth analogs of braid arrangements, appearing in robotics applications and in theory of moduli spaces of tropical curves. While their cohomology is extremely difficult to understand, and depends on...

Suppose given a class of finite combinatorial structures, such as graphs or total orders. Nate Harman and I recently introduced a notion of measure in this context: this is a rule assigning a number to each structure such that some axioms are...