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.

Add to your calendar

Download event information as iCalendar file (only this event)