Thomas Hudson

Talk 1: On a determinantal formula for the Schubert classes of the Grassmannian

A modern generalization due to Kempf and Laskov of the Giambelli-Thom-Porteous formula allows one to express every Schubert class of the Grassmannian as a determinant in Chern classes. The aim of this talk is to provide a detailed exposition of the proof of the formula, as well as a presentation of the geometric entities and constructions appearing in it: the Grassmannian, its Schubert varieties and their desingularizations.

Thomas Hudson

Talk 2: From the Chow ring to connective K-theory Alternate title: From cohomology to connective K-theory

Connective K-theory is the easiest example of an oriented cohomology theory which encodes information contained in both the Chow ring and in the Grothendieck ring of vector bundles. In this talk I will illustrate how CK* can be defined starting from algebraic cobordism, present some of its properties and finally analyze how the proof of the determinantal formula has to be modified to suit this more general context.

Tomoo Matsumura

On Pfaffian formulas for the Schubert classes of the isotropic Grassmannians

In this talk, we consider the Grassmannians of isotropic subspaces in a complex symplectic vector space. Its Schubert classes are first described by Pragacz in terms of Pfaffian in the case of cohomology of Lagrangian Grassmannians. The works of Buch-Kresch-Tamvakis, Kazarian, Ikeda, Wilson, Ikeda-Matsumura, gave its generalization to the equivariant cohomology and also to the non-maximal isotropic case. Recently, in the joint work with Hudson-Ikeda-Naruse, we obtained the analogous Pfaffian (sum) formula for connective K-theory by generalising Kazarian’s method. The aim of this talk is to review the previously existing formulas in cohomology and to explain the detail of the proof of our new formula.