QM Research Seminar: Counting Lagrangian A-branes with networks

The framework of spectral networks was introduced in physics as a way to compute BPS states of 4d N=2 gauge theories. In this talk I will review a generalization, known as exponential networks, which produces enumerative invariants associated to special Lagrangians in certain Calabi-Yau threefolds. Applications include the computation of the exact spectrum for (the mirror of) a local Hirzebruch surface. I will also sketch an alternative derivation of this framework, which elucidates the geometric meaning of the invariants in terms of elementary data of A-branes.