# 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;

*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