Open WDVV equations and manifolds with multiplication
- Date: Friday 29 March 2019, 16:00 – 17:00
- Location: Mathematics Level 8, MALL 1, School of Mathematics
- Type: Seminars, Applied Mathematics, Integrable Systems
- Cost: Free
Alexey Basalaev, National Research University Higher School of Economics, Moscow, Russia.
Classical examples of manifolds with multiplication in the tangent spaces are Frobenius manifolds, introduced in the early 90s by B. Dubrovin. Frobenius manifolds provide a geometric approach to the study of the WDVV equations -- a big system of non-linear PDEs, arising from the Gromov--Witten theory of compact Kähler manifolds. This connection was later used by C. Hertling to classify all polynomial solutions to the WDVV equations.
In our talk we will make the first steps in studying a more general system of non-linear PDEs, called the open WDVV equations, with the help of more general manifolds with multiplication. The open WDVV equations generalize the previously mentioned WDVV equations and arise from the open version of Gromov--Witten theory, that studies enumerative invariants related to Riemann surfaces with boundary.