Seminar

I will introduce the physical and mathematical context used to engineer a certain class of 4-dimensional quantum field theories, namely string theory on certain non-compact Calabi-Yau threefolds whose defining data consists of a Riemann surface with a meromorphic (or, in special cases, holomorphic) quadratic differential. Special Lagrangian submanifolds of these threefolds are related to geodesics on the corresponding flat surface; physically, they correspond to a privileged set of states, called BPS states, which I will also introduce. Finally, I will explain the physical implications for these BPS spectra of mathematical results on counts of geodesics on flat surfaces.