Apparaît dans la collection : Algebraic Analysis in honor of Masaki Kashiwara's 70th birthday

Quantum curves have been conceived in physics as a compact way to encode quantum topological invariants and solutions to certain enumerative geometry problems. In this talk, we start with describing a few concrete mathematical examples. We then present a geometric theory of quantum spectral curves of Higgs bundles. Here, the process of quantization is a passage from moduli of Hitchin spectral curves to families of Rees D-modules on a curve. The talk is based on joint papers with Olivia Dumitrescu.