Quantum cohomology via vicious and osculating walkers
Christian Korff (University of Glasgow)
Monday 4th November, 2013 16:00-17:00 Maths 204
We relate the counting of rational curves intersecting Schubert varieties of the Grassmannian to the counting of certain non-intersecting lattice paths on the cylinder, so-called vicious and osculating walkers. These lattice paths form exactly solvable statistical mechanics models and are obtained from solutions to the Yang-Baxter equation. The latter reveal a quantum group structure which induces maps between different quantum cohomology rings and can be used to compute Gromov-Witten invariants.
Time permitting we will see how this quantum group structure extends to the equivariant setting. This latter case is ongoing joint work with Vassily Gorbounov.