Algebraic Geometry Seminar: "Spectral theory, quantum curves, and topological strings"

Abstract: One current leitmotiv in mathematical physics is the idea of “quantizing” algebraic curves. In many problems whose classical limit is encoded in such a curve, it is expected that an appropriate quantization thereof can reconstruct the full theory.  One major example is local mirror symmetry, where the algebraic curve is simply the mirror curve to a toric Calabi-Yau threefold. It was conjectured some time ago that these theories can be quantized in a straightforward way, leading to trace class operators. The spectral properties of these operators contain in particular the all-genus enumerative information of the Calabi-Yau threefold. In this talk I will provide an overview of these ideas and conjectures, and I will try to list some interesting open problems. 

Host: Matt Kerr