Previous Conferences & Workshops

Hindman’s Theorem states that whenever the natural numbers are finitely coloured there exists an infinite sequence all of whose finite sums are the same colour. By considering just powers of 2, this immediately implies the corresponding result for...

Gromov--Witten invariants and Welschinger invariants count curves over the complex and real numbers. In joint work with J. Kass, M. Levine, and J. Solomon, we gave arithmetically meaningful counts of rational curves on smooth del Pezzo surfaces over...

The Prékopa-Leindler inequality (PL) and its strengthening, the Borell-Brascamp-Lieb inequality, are functional extensions of the Brunn-Minkowski inequality from convex geometry, which itself refines the classical isoperimetric inequality. These...

Q1: A fundamental result in coding theory, known as the Plotkin bound, suggests that a binary code can tolerate up to ¼ fraction of adversarial corruptions. Can we design codes that handle more errors if we allow interaction between the sender and...

Abstract: A Richardson variety R in a cominuscule Grassmannian is defined by a skew diagram of boxes. If this diagram has several connected components, then R is a product of smaller Richardson varieties given by the components. I will show that the...

Abstract: There are two major research trends in the theory of symmetric functions arising from Dyck paths. One is the theory of Catalan symmetric functions and its geometric realization conceived by Chen-Haiman, following the works of Broer and...

We resolve Manin's conjecture for all Châtelet surfaces over $Q$ (surfaces given by equations of the form $x^2 + ay^2 = f(z)$) -- we establish asymptotics for the number of rational points of increasing height. The key analytic ingredient is...

Abstract: While mirror symmetry for flag varieties and Grassmannians has been extensively studied, Schubert varieties in the Grassmannian are singular, and hence standard mirror symmetry statements are not well-defined. Nevertheless, in joint work...

Abstract: Springer fibers are subvarieties of the flag variety parameterized by partitions. They are central objects of study in geometric representation theory. Given a partition $λ$, one of the key conclusions of Springer theory is that the top...

Abstract: Suppose $X$ is the affine cone of a projective variety. The Hilbert series of the coordinate ring $C[X]$ is the character of an algebraic torus. More generally, one considers a reductive algebraic group $G$ acting rationally on $X$. When...