Abstracts

(Wormleighton): Connections between positivity of divisors in algebraic geometry and embedding problems in symplectic geometry have a ~30 year history, bringing together significant aspects of each field (e.g. Nagata conjecture, toric degenerations, ball packings,…). I will describe positivity invariants for weakly polarised surfaces that capture valuable and, in some cases, complete information about symplectic embeddings into them. I will discuss how this theory interacts with Zariski decomposition and volume of divisors, and outline the current state of the higher dimensional picture.

(Shah): For a certain class of varieties which includes partial flag varieties in type A and the permutohedral variety, we show that there exists a nonstandard Riemann-Roch theorem which interpolates between pushforwards in equivariant K-theory and equivariant cohomology. We derive some consequences, including a geometric interpretation for q-divided symmetrization. This is work in progress.

(Jeon): The Chern-Mather class introduced by MacPherson is a characteristic class, generalizing the Chern class of a tangent bundle of a nonsingular variety to a singular variety. It uses the Nash-blowup for a singular variety instead of the tangent bundle. In this talk, we consider Schubert varieties, known as singular varieties in most cases, in the even orthogonal Grassmannians and discuss the work computing the Chern-Mather class of the Schubert varieties by the use of the small resolution by Sankaran and Vanchinathan with Jones' technique. We also describe the Kazhdan-Lusztig class of Schubert varieties in Lagrangian Grassmannians, as an analogous result.

Past Seminars

Spring 2020

Autumn 2019

Spring 2019

Autumn 2018

Spring 2018

Autumn 2017

Spring 2017