Quantum Curves, Integrability and Cluster Algebras

David Wood

  •  13 Dec 2021 - 18 Dec 2021
     8:00 am - 5:00 pm

Leonid Chekhov (Michigan State University)
Paul Norbury (University of Melbourne)
Michael Shapiro (Michigan State University)
Norman Do (Monash University)
Elba Garcia-Failde (IRIF, Paris Diderot University)

Program Description:
This program will gather leading experts in the areas of quantum spectral curves, topological recursion and cluster algebras to address recent advances and proliferate new connections between these fields. Such a meeting is particularly timely as a recent connection between deformation quantisation and topological recursion by Kontsevich and Soibelman. This progress is accompanied by recent progress in quantum cluster algebras and their relation to quantum monodromies of Fuchsian systems. Connections between these fields are apparent from the physics perspective and research is now under way to make rigorous sense of these relationships.

Alexander Alexandrov (IBS Center for Geometry and Physics, Korea)
Vincent Bouchard (University of Alberta, Canada)
Alexandr Buryak (Higher School of Economics University, Russia)
Elba Garcia-Failde (Institut de mathématiques de Jussieu – Paris Rive Gauche, France)
Alessandro Giacchetto (Institut de Physique Théorique, France)
Yi Huang (Yau Mathematical Sciences Center, Tsinghua University, China)
Nick Ovenhouse (University of Minnesota, USA)
Gus Schrader (Columbia University, USA)
Anton Zeitlin (Louisiana State University, USA)

Zoom link: https://unimelb.zoom.us/j/85975689326?pwd=M3V4Z3p6dkpocUE5dGVjU3RyZ1Vsdz09
Meeting ID: 859 7568 9326
Passcode: 454532

Program Structure:
please click to expand

Click here for talk titles and abstracts

Click on the below for the talk slides
Alexandrov – KP integrability of triple Hodge integrals
Bouchard – Topological recursion, quantum curves, and atlantes Hurwitz numbers
Buryak – Counting meromorphic differentials on the Riemann sphere and the KP hierarchy
Garcia-Failde – Quantisation of spectral curves of arbitrary rank and genus via topological recursion
Giacchetto – Hurwitz theory, with (a) spin
Huang – Welcome to super hyperbolic surface theory
Ovenhouse – Double dimers and the super Ptolemy relation
Schrader – Bifundamental Baxter operators
Zeitlin – h-opers and the geometric approach to the Bethe ansatz equations

Participant List
Kowshik Bettadapura (University of Melbourne)
Anupam Chaudhari (Monash University)
Anand Deopurkar (Australian National University)
Norman Do (Monash University)
Paul Norbury (University of Melbourne)
Lukas Anagnostou (University of Melbourne)
Ellena Moskovsky (Monash University)
Michael Swaddle (University of Melbourne)
Campbell Wheeler (Max Planck Institute for Mathematics, Bonn)
Lucia Stockdale (University of Melbourne)

MATRIX Wine and Cheese Afternoon 14 December 2021
On the first Tuesday of each program, MATRIX provides a pre-dinner wine and cheese afternoon. Produce is locally-sourced to showcase delicacies from the region.