University of Washington

The distribution of rational points has been an old problem in number theory. Some of the milestones include the Mordell-Weil theorem and the Faltings’ theorem, explicitly explaining the structure of rational points on abelian varieties and on curves...

Abstract: It's well-known that any holomorphic subvariety is area-minimizing in its homology class. In this talk we consider the converse question, and we show that any entire area-minimizing 2-surface $M^2 \subset R^n$ of density two at infinity...

We consider stochastic and finite-sum optimization problems with deterministic constraints. Existing methods typically focus on finding an approximate stochastic solution that ensures the expected constraint violations and optimality conditions meet...

Abstract: This talk focuses on Richardson varieties in the complete flag variety, which are intersections of a Schubert variety with an opposite Schubert variety. Richardson varieties are indexed by intervals in the Bruhat order on the symmetric...

Squeezed balls and spheres, introduced by Kalai, form a rich class of triangulated complexes arising from subcomplexes of cyclic polytopes, with well-understood shellability properties. Recently, Novik and Zheng introduced relative squeezed balls...

The FKG inequality is a powerful tool for proving inequalities in distributive lattices. We show how a special case, which we call the Order Ideal Lemma, can be used to demonstrate a wide array of log-concavity and log-convexity results in a...

We discuss several new results on Kneser graphs. First, we define the Kneser Ramsey number R r K G ( s , t ) R r K G ​ ( s , t ) to be the minimum integer n n such that every red/blue edge-coloring of the Kneser graph K G ( n , r ) K G ( n , r )...

Formal schemes were introduced by Grothendieck to geometrize the idea of taking the completion of a ring which corresponds to taking “formal” analytic / power series functions around a closed subset. They find a lot of use in deformation theory in...

I will try to give a high-level overview of Clausen-Scholze’s theory of light condensed mathematics with a view toward its structure in the solid setting. In the end, the resulting setup of solid analytic stacks provides a uniform framework for...