A geometric Littlewood–Richardson rule
We describe a geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties into the union of Schubert varieties. There are no restrictions on the base...
View ArticleSchubert induction
We describe a Schubert induction theorem, a tool for analyzing intersections on a Grassmannian over an arbitrary base ring. The key ingredient in the proof is the Geometric Littlewood-Richardson rule...
View ArticleInvariant measures and the set of exceptions to Littlewood’s conjecture
We classify the measures on $SL(k,\mathbb{R}) / SL(k,\mathbb{Z})$ which are invariant and ergodic under the action of the group $A$ of positive diagonal matrices with positive entropy. We apply this to...
View ArticleHigher genus Gromov–Witten invariants as genus zero invariants of symmetric...
I prove a formula expressing the descendent genus $g$ Gromov-Witten invariants of a projective variety $X$ in terms of genus $0$ invariants of its symmetric product stack $S^{g+1}(X)$. When $X$ is a...
View ArticleCombinatorics of random processes and sections of convex bodies
We find a sharp combinatorial bound for the metric entropy of sets in $\mathbb{R}^n$ and general classes of functions. This solves two basic combinatorial conjectures on the empirical processes. 1. A...
View ArticleDeligne’s integrality theorem in unequal characteristic and rational points...
If $V$ is a smooth projective variety defined over a local field $K$ with finite residue field, so that its étale cohomology over the algebraic closure $\bar{K}$ is supported in codimension 1, then the...
View Article
