Geometry and Physics of Quantum Curves (18w5078)

Arriving in Banff, Alberta Sunday, September 9 and departing Friday September 14, 2018

Organizers

(University of California, Davis)

(University of Toronto)

(Central Michigan University)

(University of Pennsylvania)

Objectives

When mysteries arise, the first task we need to do is to understand exactly what is going on. We focus on the following three topics in the workshop:



  1. Spectral theory in mirror symmetry and quantum curves;
  2. Airy structures and quantization of moduli spaces;
  3. Geometry of quantum curves and WKB analysis.




The central theme of (1) is the Grassi-Hatsuda-Mari\~no conjecture. (2) concerns Airy structures and complex Chern-Simons theory on a projective curve. (3) is the geometric framework of quantization of Hitchin spectral curves in terms of opers.



The goal of the workshop is to establish a mathematical understanding of the mysteries surrounding these three topics. They have been developed completely independently, yet are believed to be deeply related one another.



In the workshop, we invite the key players of these three topics. Already the organizers have received enthusiastic response from them, thanking for the opportunity to interact that we are creating through the proposed BIRS workshop.



These three topics were also among many other subjects discussed in the String-Math 2016 that was held in Coll\`ege de France, Paris, in June-July 2016. The plenary speakers talked on the above themes were: Mari\~no on (1), Kontsevich on (2), and Dumitrescu on (3). Their presentations generated strong excitements among the participants. Allocating the whole week and focusing on specific topics, we expect a rich interactive outcome from the proposed workshop.



We plan to invite graduate students, postdoctoral scholars, and pre-tenure faculty members to the workshop. Since the key players of the proposed topics include women scientists in their early careers (Olivia Dumitrescu in algebraic geometry, Laura Fredrickson in geometric analysis, and Alba Grassi in theoretical physics), we expect that the proposed workshop will also inspire young women participants.