Integrable Systems, Liouville Foliations, and Nijenhuis Geometry

August 11–15, 2025, CIMAT Guanajuato

Organisers:

Sonja Hohloch (Antwerp), Vladimir S. Matveev (Jena)

Participation:

The workshop is by invitation only. If you would like to participate, please contact the organisers.

Description:

This is a “working workshop,” meaning that we will have only a few talks, with a strong emphasis on collaborative research in small groups (typically 2–4 participants from different institutions).

The general goal is to study Liouville foliations and their singularities in integrable systems. We aim to promote collaboration between various research groups by combining different methods and perspectives.

A particular focus will be on the Liouville foliations and singularities arising in finite-dimensional reductions of known infinite-dimensional integrable systems. Through a deeper understanding of these structures, we aim to gain new insights into the dynamics of such systems. We also plan to construct new exact solutions or better understand classical ones. Additionally, we will address the quantization of these infinite-dimensional systems via their finite-dimensional reductions.

Special attention will be given to the so-called BKM infinite-dimensional integrable systems, which are developed within the framework of the Nijenhuis geometry program. These systems include, as particular cases, many well-known and widely studied equations such as KdV, DWW, Camassa-Holm, Antonowicz-Fordy, and others. We hope that methods developed for these systems can be generalized to the broader class of BKM systems.

Preliminary List of Participants:

  • D. Akpan (Jena)
  • J. Bernatska (Connecticut)
  • A. Bolsinov (Loughborough)
  • T. Henriksen (Antwerp)
  • C. Huiszoon (Antwerp)
  • S. Ignoul (Antwerp)
  • V. Kibkalo (Moscow)
  • A. Konyaev (Moscow)
  • M. Manenti (Antwerp)
  • K. Marciniak (Lund)
  • K. A. Nguyen (Melbourne)
  • A. Oshemkov (Moscow)
  • J. Palmer (Amherst)
  • G. Palshin (Sydney)
  • M. Quaschner (Jena)
  • P. Santos (Antwerp)
  • S. Scapucci (Jena)
  • W. Steneker (Tromsø)
  • P. Topalov (Boston)
  • Zhijun Qiao (Edinburg, US)