Takeshi Ikeda's lecture 1:

The aim of the first lecture is to provide some general ideas in Schubert calculus, and set up some notation related to Grassmannian. I will start from a typical question in enumerative geometry. How many lines that intersect four given lines in the 3-space? The answer is given in an intuitive way that motivates the main part of the lecture. 

Takeshi Ikeda's lecture 2:

I will try to explain some basic facts on intersection theory of Grassmannian. It includes the duality theorem and Pieri rule. I first formulate the intersection ring of Grassmannian by introducing some formal symbols associated with Schubert varieties. The product structure can be defined by counting the number of triple intersection of Schubert varieties. As a special case, I will show how we can actually count the intersection numbers, which leads to the Pieri rule. 

Takeshi Ikeda's lecture 3:

I will connect the geometric idea developed in the previous lectures with the ring of symmetric functions. In fact, each Schubert class is identified with the Schur function. One of the goal of the lecture is a proof for the so-called Littlewood-Richardson rule, which describes the triple intersection numbers in general. 

Takeshi Ikeda's lecture 4:

By introducing the notion of Chern classes, I will show how to solve further enumerative problem. For example, I will consider the question “How many lines lying on a general cubic surface?”. In the last part, I will discuss how we can extend the story to other geometric invariants like torus equivariant cohomology, K-theory, and quantum cohomology etc. And also I will discuss natural extension of Schubert calculus for more general homogeneous varieties. 

Dang Tuan Hiep's tutorials 1 and 2:

Accordingly with the lectures of Takeshi Ikeda, I will introduce two computational methods in Schubert Calculus and packages for computer algebra systems. The first package for Maple called “Schubert" was written by Sheldon Katz and Stein Arild Strømme from 1992. However, this package is no longer actively supported, and current efforts have moved from Maple to Macaulay2 called “Schubert2”. In these tutorials, I will introduce two efforts building on Schubert Calculus called “Schubert3” for SageMath and “schubert.lib" for Singular and present how to use them. 

Dang Tuan Hiep's lecture 1: Hirzebruch-Riemann-Roch formula

This lecture will cover the theory characteristic classes of vector bundles on algebraic varieties. As a central theme, I will formulate the Hirzebruch-Riemann-Roch formula that allows us compute the Euler characteristic of a vector bundle via intersection theory.

Dang Tuan Hiep's lecture 2: Tango bundles on Grassmannians

An interesting vector bundle on the complex projective space, which is indecomposable, was constructed by Tango in 1976. Recently, by using Schubert calculus, Costa, Marchesi and Miró-Roig proved the existence of such vector bundles on Grassmannians. This lecture will recall these results and present the Euler characteristic of the Tango bundles.