In this 3 hours lecture, I will try to cover the following topics.

강의 1, Jan 19, Monday, 2:00pm - 3:00pm
강의 2, Jan 19, Monday, 3:20pm - 4:20pm
강의 3, Jan 20, Tuesday, 11:00 am - 12:00 pm.

(1) An introduction to Schubert calculus: Grassmannians, Schubert classes, e.t.c.

(2) A modern generalization due to Kempf and Laskov of the Giambelli-Thom-Porteous formula: a formula to express every Schubert class of the Grassmannian as a determinant in Chern classes. I will explain a geometric proof of this formula using certain desingularizations of the Schubert varieties for Grassmannians.

(3) Connective K-theory CK^*: 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. I will illustrate how CK* can be defined starting from algebraic cobordism, present some of its properties.

(4) I will explain how the proof of the determinant formula in cohomology can be generalized to K-theory.
This lecture is based on a joint work with T. Thomas, T. Ikeda and H. Naruse.