Isomonodromic Deformations
Painlevé Equations, and
Integrable Systems

Columbia University (online), June 27–July 1, 2022


Integrable systems played an extremely important role in mathematical physics over the last 50 years. Their physical applications include gauge theories and conformal field theories, as well as statistical models. Mathematically, this area has deep connections with complex and algebraic geometry, geometry of algebraic curves and various types of moduli problems. Among the key tools of the modern theory of integrable system is the notion of a Lax Pair representation or, equivalently, of an isospectral deformation of some linear problem – the associated spectral curve then encodes the integrals of motion of the system. The non-autonomous analogue of this representation is the notion of an isomonodromic deformation. Classical theory of isomonodromic deformations goes back over a hundred years to the works of Fuchs and Schlesinger. It was revived in mid-1980s by the Japanese school, and at present it is yet again attracting a lot of attention. Classical connections between isomonodromic deformations and differential Painlevé equations have been generalized to the discrete case. There are deep connections of this area to new exciting mathematical objects such as Integrable Probability, Cluster Varieties and Dimer Models, as well as the relations between tau-functions of differential Painlevé equations and Conformal Blocks, and its generalization to q-Painlevé equations. And the list goes on. The goal of our conference is to discuss some of the recent progress and results in this exciting area of Mathematical Physics.


  • Marco Bertola (Concordia University, Montreal, Canada and SISSA, Trieste, Italy)
  • Alexander I. Bobenko (Institut für Mathematik, Technische Universität Berlin, Germany)
  • Alexei Borodin (Massachusetts Institute of Technology, Cambridge, MI, USA)
  • Thomas Bothner (King’s College London, London, UK)
  • Mattia Cafasso (Université d'Angers, Angers, France)
  • Philippe Di Francesco (University of Illinois at Urbana-Champaign, Urbana, IL, USA)
  • Vladimir Fock (Université de Strasbourg et CNRS, Strasbourg, France)
  • Alexander Goncharov (Yale University, New Haven CT, USA)
  • Alba Grassi (Université de Genève and CERN, Geneva, Switzerland)
  • Rod Halburd (University College London, London, UK)
  • Alisa Knizel (University of Chicago, Chicago, IL, USA)
  • Peter Miller (The University of Michigan, Ann Arbor, MI, USA)
  • Nikita Nekrasov (Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY, USA)
  • Masatoshi Noumi (Rikkyo University, Tokyo, Japan)
  • Axel Saenz (Oregon State University, Corvalis, OR, USA)
  • Leon Takhtajan (Stony Brook University, Stony Brook, NY, USA and Euler Mathematical Institute, Saint Petersburg, Russia)
  • Yasuhiko Yamada (Kobe University, Kobe, Japan)

Organizing Committee

  • Mikhail Bershtein (Landau Institute, Skoltech, Higher School of Economics, Moscow, Russia)
  • Anton Dzhamay (The University of Northern Colorado, Greeley, CO, USA)
  • Pavlo Gavrylenko (Université de Genève, Geneva, Switzerland and Skoltech, Moscow, Russia)
  • Igor Krichever (Columbia University, New York, NY, USA and Skoltech, Moscow, Russia)
  • Andrei Marshakov (Skoltech, Higher School of Economics, Lebedev Institute, Moscow, Russia)