Abstract
(for two lectures): My subject is Schubert varieties and
their classes. I shall speak about some
combinatorial rules for multiplication of Schubert
classes in cohomology rings of flag varieties. I will
also give a sketch of a recent proof by J. Huh of the
positivity conjecture for Chern classes of Schubert
cells and varieties in Grassmannians. Here is a
more detailed plan:

Lecture 1: Semisimple groups, Borel subgroups, Tori, Weyl groups,

Root systems, Schubert varieties and classes, structure constants

of multiplication in the basis of Schubert classes, characteristic map, BGG-operators, the Chevalley formula.

Lecture 2: Littlewood-Richardson rule, Knutson-Tao puzzles , hives,...

An outline of Huh's proof.

Lecture 1: Semisimple groups, Borel subgroups, Tori, Weyl groups,

Root systems, Schubert varieties and classes, structure constants

of multiplication in the basis of Schubert classes, characteristic map, BGG-operators, the Chevalley formula.

Lecture 2: Littlewood-Richardson rule, Knutson-Tao puzzles , hives,...

An outline of Huh's proof.