Speaker: Sergey Galkin

Title: Hyperkähler manifolds and modular forms

Date: Dec 21-22, 2015, 12:30-13:30

Place: NoGAGS, Freie Universität, Berlin

One-dimensional moduli spaces of lattice-polarised hyperkähler manifolds tend to be the usual modular curves with respect to some congruence subgroups in SL(2,R), and the periods of the respective Picard-Fuchs equations are the usual modular forms. First of all, this suggests that the respective hyperkähler manifolds with large Picard number are isogeneous to powers of elliptic curves, similarly to the theory of Inose-Shioda and Morrison. Also mirror symmetry together with explicit computations of the respective differential equations and periods might help with providing new constructions of hyperkähler manifolds polarised by a single ample divisor.