Center Seminar on Mondays

Center for Advanced Studies Seminar on Mondays at 14.30 at Skoltech

March-April, 2018
Nikolai Tyurin
(JINR Dubna, HSE)
Special Bohr-Sommerfeld geometry of algebraic varieties

Every algebraic variety can be regarded as a real symplectic manifold. Therefore it can be studied as a symplectic manifold, in particular one can study lagrangian geometry of it. In contrast with algebraic geometry, real lagrangian geometry is not rigid, and if we want to construct finite dimensional moduli spaces of lagrangian submanifolds we must impose certain condition on these ones. The brilliant example exists for Calabi – Yau manifolds: Hitchin and McLean constructed finite dimensional moduli space of special lagrangian submanifolds, which has been exploited in SYZ conjecture for explanations of Mirror Symmetry. I present first results from the programme, based on Andrey Tyurin’s works on Bohr – Sommerfeld lagrangian cycles. Introducing new specialty condition on Bohr – Sommerfeld lagrangian submanifolds we construct finite dimensional moduli spaces for arbitrar compact simply connected algebraic variety with a fixed polarization