Nagoya IAR workshop on

Unification of Integrable Systems

27〜29 October, 2025 at Nagoya University and Online

This workshop is co-sponsored by Institute for Advanced Research (IAR), Nagoya U.

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Questionnaire for the workshop(アンケート)
We would appreciate your cooperation!

• Scope: The main topics of this workshop are the four-dimensional Chern-Simons (4dCS) theory and the four-dimensional Wess-Zumino-Witten (4dWZW) model which might shed light on a way of unification if integrable systems. Recently Costello, Yamazaki and Witten found that the 4d Chern-Simons theory is a master theory of many solvable models such as spin chains and principal chiral models by pursuing an origin of their spectral parameters. This leads to new developments in the study of solvavle models and many subsequent works have been done. On the other hand, the 4dWZW model relates to another kind of integrable systems. Equation of motion of the 4dWZW model is the Yang equation which is equivalent to the anti-self-dual Yang-Mills (ASDYM) equation. It is well known for the Ward conjecture that the ASDYM equations can be reduced to many classical integrable systems, such as the KdV eq., Toda eq. and Painleve eqs (mostly in the split signarture). Furthermore, the 4dWZW model describes the space-time action of the open N=2 string theory in the four-dimensional space-time with the split signature.
  As suggested by Costello, Bitteleston and Skinner showed that these two theories (4dCS and 4dWZW) are derived from a six-dimensional Chern-Simons (6dCS) theory like a ``double fibrations'' as in the above figure. This fact would imply nontrivial duality correspondences between the 4dWZW model and the 4dCS theory (and between their descendants). Hence a unified theory of integrable systems (6dCS→4dCS/4dWZW) can be proposed (in the split signature). Now it is time to clarify the current situations and unsolved problems and to elucidate future directions and new interpretations to the theory of solvable models and integrable systems.
  This workshop will be held to gather relevant speakers and to have fruitful discussions with participants related to the unification of integrable systems. The above scenario would be just a slice of unified theory of integrable systems. Other aspects such as 4d/5d/6d Chern-Simons theories, (affine) Gaudin models, Lagrangian multi-form theory etc. are also discussed. In the panel discussion, we plan to discuss perspectives of unification of integrable systems and recent interaction between physics and mathematics etc. We might pick up good questions from the registration forms and introduce them at the panel session.
  

• Date: 27th(Mon)〜29th(Wed) October 2025
  

• Place: Sakata-Hirata Hall, Nagoya University (D2-7 on the map) (← Search `Sakata')

• Speakers: Talk title[Video][Slide] (Abstracts are here)
  
  • Benoit Vicedo (York): Lax integrability and holomorphic-topological gauge theory [Video]

  • Masahito Yamazaki (Tokyo): Generalized Chiral Potts Models and Hyperbolic Monopoles from Chern-Simons Theories [Video]

  • Kentaroh Yoshida (Saitama): The Courant-Hilbert construction in 4D Chern-Simons theory [Video][Slide(Part2)]

  • Hiroaki Matsunaga (Osaka): Homotopy algebraic approach to Lagrangian multiform

  • Masashi Hamanaka (Nagoya): Towards Unification of Integrable Systems -- from ASD Yang-Mills viewpoints [Video][Slide]

  • Panel Discussion: B.Vicedo(Panelist), M.Yamazaki(Panelist), K.Yoshida(Panelist), M.Hamanaka(interviewer) [Video][Slide]

• Program (Time zone is the Japan Standard Time (JST))
  

  	Oct.27(Mon)	Oct.28(Tue)	Oct.29(Wed)
  11:00〜12:00		Yamazaki	NONE
  13:30〜15:00	Vicedo	Vicedo	Vicedo
  15:30〜16:30	Yamazaki	Yoshida	Yoshida
  16:45〜17:45	Hamanaka	Panel Discussion#	16:30〜17:00 Matsunaga

  (#) Panelists: B.Vicedo, M.Yamazaki, K.Yoshida, ..., M.Hamanaka(interviewer)

Remarks

• Accommodation: We don't arrange accommodation for any participants. Please book it by yourself... If you receive an email from organizers or someone about accommdation, it must be spam and ignore it.
  cf. [Rakuten Travel(Japanese)] [Rakuten Travel(English)]
  

• Questions: Audiences can ask a question at any time. (Online participants can unmute their mic to ask a question or write a chat message on Zoom.)

• Video Recording: Talks will be recorded and uploaded to Youtube. If you don't want to make your question to be public, please send an email to organizer: hamanaka~AT*math.nagoya-u.ac.jp. (Then the relevant part of the video will be trimmed.)

Organizers: Masashi Hamanaka, Hiroaki Kanno, Shintaro Yanagida

Last Update: 7 November 2025