Noncommutative Integrable Systems

• Scope: Integrable systems have been studied intensively for the last several decades interacting with representation theory, combinatorics and physics. Noncommutative extension of them have also been one of the main topics, such as, extension to matrix valued systems, to noncommutative spaces and so on. As for construction of exact solutions of the noncommutive integrable systems, quasideterminants play crucial roles. Quasideterminants are first introduced by I.M. Gelfand and V. Retakh in 1991. (For a good survey, see e.g. I. Gelfand, S. Gelfand, V. Retakh, R. Wilson, ``Quasideterminants.'') Many achievements have been made over the next 30 years, however, there are many things to be seen: especially in integrable systems, theory of noncommutative tau-functions, noncommutative Pfaffians and so on. It is time to review the developments from various viewpoints, to clarify important problems and discuss further perspectives. This workshop is held to achieve these objectives. The first week is arranged to be a school for students and non-experts on these topics and the second week is mostly devoted to research talks contributed by registered speakers. The topics cover noncommutative integrable systems (e.g. matrix valued systems, integrable systems on noncommutative spaces, noncommutative solitons and quantum integrable systems) and related mathematics and physics.

• Date: March 4 〜 March 15, 2024 (Totally six days)

• Place：Zoom platform: Zoom link is here (passcode:quasidet)
  Zoom link will be shown here 2 hours before the start of the first talk. (In the case that this website is dead, it will be displayed at the researchseminars org .)

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

  Mar.05(Tue)	Mar.07(Thu)	Mar.08(Fri)
  9:30〜10:30 Retakh	9:30〜10:30 Retakh	9:30〜10:30 Retakh
  17:00〜18:00 Bobrova	17:00〜18:00 Bobrova	17:00〜18:00 Roubtsov

  Mar.11(Mon)	Mar.13(Wed)	Mar.15(Fri)
  17:00〜17:45 Carillo	9:30〜10:30 Berenstein	17:00〜18:00 C.-X. Li
  18:00〜19:00 Gilson		18:15〜19:15 Kanomata Okuda
  19:30〜21:00 Tanaka Razavinia Skopenkov	17:00〜18:00 Sharygin Ikeda	19:30〜21:00 S. Li Amano Sergyeyev

  • In the week of March 4th, Mar 5, 9:30am (JST)=Mar 5, 8:30am (China)=Mar 5, 1:30am (EU)=Mar 5, 0:30am (UK)=Mar 4, 7:30pm (NewYork)=Mar 4, 4:30pm (Oregon, Calfornia)
  • In the week of Mar 11th (US is in summer time), 17:00 (JST)=16:00 (China)=9:00 (EU)=8:00 (UK)= 4:00 (NewYork)=1:00 (Oregon, California)
  • Sessions of research talks will be held on three days in the week of March 11. Each session on one day consists of several 20-30 min. talks by applied people.

• Invited Speakers: Title [Abstract]
  
  • Arkady Berenstein (Oregon): Noncommutative surfaces, clusters, and their symmetries [Abstract] [Slide] [Video]
  • Irina Bobrova (MPI): Non-Abelian ODEs and OΔEs [Abstract] [Slide] [Video(Mar.5)] [Video(Mar.7)]
  • Sandra Carillo (Roma): Backlund transformations and non-Abelian nonlinear evolution equations [Abstract] [Slide]
  • Claire Gilson (Glasgow): Pfaffian Solutions to Non-Commutative Integrable Systems [Abstract] [Video]
  • Chun-Xia Li (Beijing): On construction and integrability of the noncommutative extended KP equation and the noncommutative extended mKP equation [Abstract] [Slide] [Video]
  • Vladimir Retakh (Rutgers): Quasideterminants and their applications. An introduction I, II, III [Slide I] [Slide II] [Slide III] [Video I] [Video II] [Video III]
  • Volodya Roubtsov (Angers): Painleve equations -- different facets of non-commutativity [Abstract] [Slide] [Video]

• Research Talk Speakers: Titles [Abstract]
  • (Mar.11) M. Tanaka: Solvability and nilpotency of Kac--Paljutkin's finite quantum group and Sekine quantum groups [Abstract] [Slide]
  • (Mar.11) F. Razavinia: Into multiplier Hopf Graph Algebras and beyond [Abstract] [Slide]
  • (Mar.11) M. Skopenkov: Noncommutative exterior product in lattice integrable systems [Abstract] [Slide]

  • (Mar.13) G. Sharygin: Argument shift method in the algebra Ugl(n) [Abstract] [Slide]
  • (Mar.13) Y. Ikeda: Quantum analog of Mishchenko-Fomenko theorem for Ugl_d [Abstract] [Slide]

  • (Mar.15) N. Kanomata: Calogero Model from Real Symmetric φ⁴ Matrix Model as a Noncommutative Scalar Field Theory [Abstract] [Slide]
  • (Mar.15) T. Okuda: Noncommutative G_2,4(C) as Deformation Quantization with Separation of Variables [Abstract] [Slide]

  • (Mar.15) S. Li: Solutions to the SU(N) self-dual Yang-Mills equation [Abstract] [Slide]
  • (Mar.15) M. Amano: Non-Linear Deformed Holographic Abelian-Higgs Vortices [Abstract] [Slide]
  • (Mar.15) A. Sergyeyev: Multidimensional integrable systems from contact geometry [Abstract] [Slide]

Registration

• Participation needs no registration. Research talk application has been closed. If you are still interested in it, please email to an organizer.

Remarks

• Invited talks are mostly 60 minites + discussion, but could be flexibly extended.
• Audiences can have a question at any time by unmuting their mic or by writting a chat message.
• Invited 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 (See below). Then the relevant part of the video will be trimmed.
• Talk slides will be uploaded in this homepage if the speakers agree.
• This workshop is supported by the Ichihara International scholarship foundation.

Organizers: Masashi Hamanaka (Nagoya) (E-mail: hamanaka AT math.nagoya-u.ac.jp, where AT should be replaced with @), Shan-Chi Huang (Nagoya) and Shintaro Yanagida (Nagoya).

Last Update: July 17, 2024.