Memorial University of Newfoundland

 

Atlantic Association for Research in the Mathematical Sciences

Atlantic Algebra Centre 

Introduction to
Schubert calculus
via (nil-)Hecke algebras

 

Mini-course by

Professor Kirill Zaynullin

University of Ottawa

September 21 - 23, 2021

From September 21 to September 23, 2021, Professor Kirill Zaynullin from the University of Ottawa will give an introductory mini- course on nil-Hecke algebras and their applications in cohomology.

The mini-course will consist of four lectures and will give a self-contained exposition on the use of the techniques of nil-Hecke algebras in the equivariant Schubert calculus for cohomology of flag varieties.

The first part will discuss root datum and Coxeter groups (Lectures 1-2): definition of a root datum, simple roots, fundamental weights and the Cartan matrix, the Dynkin diagram, the Weyl group, geometric realization, finite real root systems, coefficient ring of a root system, non-crystallographic root datum.

The second part will introduce nil-Hecke rings and twisted group algebras (Lectures 2-3): definition of nil-Coxeter and nil-Hecke rings, twisted group algebras and their localizations, coproducts, Hecke and Weyl actions, characteristic and the Borel maps. 

The third part (Lectures 3-4) will relate nil-Hecke rings and the Schubert calculus techniques: push-pull elements and divided- difference operators, the coproduct and the actions, faithful representation, the augmented coproduct and the formula for the coproduct, the dual of the nil-Hecke ring and equivariant cohomology. 

The lectures will take place at the St. John's campus of Memorial University and will be broadcast via Zoom. The schedule is as follows in Newfoundland Time:

Tuesday, September 21, 9:30-10:20 am (Lecture 1 recording)and 3:30-4:20 pm (Lecture 2 notes);

Wednesday, September 22, 9:30-10:20 am (Lecture 3 recording);

Thursday, September 23, 9:30-10:20 am (Lecture 4 recording).

The room is HH-3015 or join via Zoom (Meeting ID: 942 3704 5057, Passcode: UFbd7s)