# 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 8
- Quantum cohomology of Grassmannians
- Till Wehrhan
- December 15
- Quantum cohomology of (co)minuscule varieties
*tbd*- January 5
- Fusion rings, Verlinde algebras and quantum cohomology (I)
- Catharina Stroppel
- January 12
- Fusion rings, Verlinde algebras and quantum cohomology (II)
- Catharina Stroppel
- January 19
- The isotropic Grassmannian $\mathrm{IGr}(2,6)$
*tbd*- January 26
- Lefschetz collections and the structure of quantum cohomology
*tbd*