Integrability, Q-systems and Cluster Algebras

August 11, 2024 - August 18, 2024

The event is organized by the International Centre for Mathematical Sciences (ICMSSofia) at the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences with the financial support of Simons Foundation.

Organizers: Ivan Todorov, Ivan Kostov, Valentina Petkova, Vesselin Filev, Todor Popov,  Radoslav Rashkov,  Neli Stoilova, Tzvetan Vetzov

By integrability one understands the collection of techniques from a variety of mathematical disciplines such as algebra, representation theory, geometry and topology, developed to solve integrable systems. The applications of integrability are numerous and are not restricted to mathematical and theoretical physics. For instance, orthogonal circle patterns which give a discretisation of conformal maps and are governed by integrable equations, have been used to construct elements in architecture.

This workshop focuses on integrable models that can be described in terms of quantum spectral curves (QSC). A QSC is a solution of the Q-system, a system of non-linear recurrence relations characterising the integrable model. Some Q-systems are in turn related to the cluster algebras which have been intensely studied in the last two decades.   Cluster structures appear in the Seiberg-Witten systems describing the infrared behaviour of N=2 supersymmetric Yang-Mills theory.

The aim of the workshop is to bring together mathematicians and theoretical physicists to discuss and explore geometric, algebraic, and computational aspects of the QSC and the relation with cluster systems.

Students and young scientists, both theoretical physicists and mathematicians, interested in integrability are encouraged to participate. Lectures for students and non-specialists are planned in view of improving the research capacity of the Bulgarian scientists.


Expected Participants:

Hrachya Babujian (Erevan Physics Institute))

Benjamin Basso (ENS Paris)

Alexander Bobenko (Techniche Universitet Berlin)

Nikolay Bobev (University Leuven)  

Hermann Boos (University of Wuppertal)

Dmitry Chernyak – PhD (ENS)  

Philippe Di Francesco (IPhT Saclay and University of Illinois)  

Michael Douglas (Harvard University)

Nikolay Gromov (Kings College London)

Iva Halacheva (Northeastern U.)

Vladimir Kazakov (ENS, Paris)

Rinat Kedem (University of Illinois)

Andreas Klümper (University of Wuppertal)

Grisha Korchemsky (IPhT Saclay)

Gleb Kotousov (Leibniz University Hannover)

Jesper Jacobsen (ENS Paris)

Fedor Levkovich-Maslyuk

Davide Masoero (University of Lisbon)

Stefano Negro (NYU)

Enrico Olivucci (Perimeter Institut)

Vincent Pasquier

Ana Retore (Durham U)  

Volker Schomerus (DESY Hamburg)  

Didina Serban (CEA Saclay)  

Fedor Smirnov (Paris Sorbonne)

Milen Yakimov (Northeastern U.)

Kostya Zarembo (Nordita)

Published On: September 26, 2023Categories:
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