School of Mathematics

We show that skein valued counts of open holomorphic curves in a symplectic Calabi-Yau 3-fold with Maslov zero Lagrangian boundary condition are invariant under deformations and discuss applications (Ooguri-Vafa conjecture and simple recursion...

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...

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...

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 Picard...

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 Shimozono...

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 X is matrix space...

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 with...

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 dimensional...

Chow quotients of projective varieties by affine torus actions provide alternative constructions of interesting geometric objects. For example, the moduli space of stable genus 0 curves with n

marked points arises as the Chow quotient of the...