Master´s degree project: Computation of superpotentials of monotone Lagrangian submanifolds in Kähler manifolds

Abstract: We compute the superpotentials of the monotone twist Lagrangian tori in products of complex projective lines, as defined by Chekanov and Schlenk. The superpotential of a monotone Lagrangian submanifold is a generating function whose coefficients encode counts of pseudo-holomorphic discs with boundary on the Lagrangian, and with Maslov index equal to 2. The calculation uses several tools from complex analysis.