# Quantum cohomology of partial flag varieties

In the Wintersemester 2020–2021 we will run a seminar on quantum cohomology of partial flag varieties, introducing a second theme to the symphony which is the geometry of partial flag varieties (the first theme being the structure of the derived category, as discussed in the previous seminar). The goal is to:

• introduce quantum cohomology, as a deformation of the usual cohomology of a variety using Gromov–Witten invariants;
• describe methods to work with the quantum cohomology of partial flag varieties;
• give structural results of the quantum cohomology of partial flag varieties, and understand their link to the structure of the derived category;
with a view towards current research. For the majority of the time the previous seminar is not a prerequisite.

We have a detailed program.

Where? via Zoom, the link will be distributed to the local participants
When? on Tuesdays, from 4 to 6

November 3
Dubrovin's conjecture
Pieter Belmans
November 10
Geometric preliminaries and presentation of the black boxes
Pieter Belmans
November 17
Gromov–Witten invariants
Ji Zekun
November 24
Big quantum cohomology
Till Wehrhan
December 1
Small quantum cohomology
Till Wehrhan
December 7–10
Exceptional collections on homogeneous varieties of simple algebraic groups
Alexander Kuznetsov, as part of Workshop on moduli spaces and stability
December 15
Quantum cohomology of Grassmannians
Till Wehrhan
January 5
Quantum Schubert calculus
Pieter Belmans
January 12
question session
January 19
Quantum cohomology of cominuscule Grassmannians
Nicolas Perrin (Université de Versailles Saint-Quentin)
January 26
Fusion rings, Verlinde algebras and quantum cohomology
Catharina Stroppel
February 2
The isotropic Grassmannian $\mathrm{IGr}(2,6)$
Maxim Smirnov (Universität Augsburg)
February 9
Lefschetz collections and the Kuznetsov–Smirnov conjecture
Pieter Belmans