Title: |
Clifford algebras and quantum cohomology |

Speaker: |
Christian Korff (Glasgow) |

Abstract: |
The quantum cohomology ring of the complex Grassmannian first appeared in works by Gepner, Vafa, Intriligator and Witten and a particular specialisation of it can be identified with the fusion ring of the gauged $\widehat{gl}(n)$-WZNW model. The talk will focus on how one derives known (geometric) results about the quantum cohomology ring in a simple combinatorial setting using well-known techniques from quantum integrable systems. It turns out that the fundamental object to describe the quantum cohomolgy ring is a finite dimensional Clifford algebra (free fermions in physics language). This free fermion formalism allows one to derive new results such as recursion relations for Gromov-Witten invariants and a fermion product formula. |