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# Olivia Dumitrescu, Central Michigan University – Job Talk

## February 25, 2020 @ 4:00 pm - 5:00 pm

**Title:** From quantization to holomorphic Lagrangian geometry

**Abstract: **Sir George Biddel Airy discovered the rainbow integral and explained the classical analysis of rainbows. 150 years later, Kontsevich found that the same formula determined the

multiplication table of cohomology classes on the compactified moduli spaces of Riemann surfaces. These stories are a simple example of a mathematical theory of “quantum curves.” I will present a general framework of quantum curves and I will relate it to a conjecture of Davide Gaiotto (2014) in physics regarding “conformal limits”. The oper case of this conjecture is due to Fredrickson, Kydonakis, Mazzeo, Mulase, Neitzke and myself and was generalized by Collier and Wentworth.

I will present an algebraic geometry description of the Lagrangian correspondence of Gaiotto, based on the work of Simpson. This talk is based on joint work with Motohico Mulase.