BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Benoit Vicedo (York) DTSTART:20251027T043000Z DTEND:20251027T060000Z DTSTAMP:20260404T095717Z UID:UIS2025/1 DESCRIPTION:Title: Lax integrability and holomorphic-topological gauge theory (Lecture 1)\nby Benoit Vicedo (York) as part of Nagoya IAR workshop on Unifica tion of Integrable Systems\n\nLecture held in Sakata-Hirata Hall\, Nagoya University.\n\nAbstract\nThe Lax formalism provides a powerful and unifyin g framework for describing classical integrable field theories in various spacetime dimensions. Its central object\, the Lax matrix\, depends on the spacetime coordinates and meromorphically on an auxiliary complex variabl e known as the spectral parameter.\n\n\n\nIn a series of recent seminal wo rks\, Costello\, Witten and Yamazaki have shown that the Lax formalism adm its a natural and elegant geometric origin in higher-dimensional holomorph ic-topological gauge theory. In this setting\, the spectral parameter is i ncorporated into the spacetime geometry and the Lax matrix arises as a spe cific component of the gauge field.\n\n\n\nIn these lectures I will give a n introduction to this connection between the Lax formalism and holomorphi c-topological gauge theories.\n\n\n\nLecture 1 - (1d IFTs) Lax pairs encod e the integrable structure of finite-dimensional integrable systems\, i.e. 1-dimensional integrable field theories\, such as the closed Toda chain o r the Gaudin model on a product of coadjoint orbits. After reviewing this formalism\, I will explain how the framework of spectral parameter depende nt Lax pairs naturally emerges from 3-dimensional holomorphic-topological BF theory.\n\n\n\nLecture 2 - (2d IFTs) Lax connections are an affine gene ralisation of Lax pairs which encode the integrable structure of 2-dimensi onal integrable field theories. I will review their deep connection to aff ine Gaudin models in the Hamiltonian formalism and explain how 4-dimension al holomorphic-topological Chern-Simons theory captures the same structure from a Lagrangian perspective.\n\n\n\nLecture 3 - (≥ 3d IFTs) In 3 dime nsions and above there is no general\, universally accepted definition of integrability. I will explain how the framework of holomorphic-topological gauge theories in 5-dimensions and above can be used as a guiding princip le for formulating appropriate higher-dimensional analogues of Lax integra bility. In particular\, I will introduce 5-dimensional holomorphic-topolog ical 2-Chern-Simons theory as a potential higher gauge-theoretic framework for describing 3-dimensional integrable field theories.\n LOCATION:https://stable.researchseminars.org/talk/UIS2025/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Masahito Yamazaki (Tokyo) DTSTART:20251027T063000Z DTEND:20251027T073000Z DTSTAMP:20260404T095717Z UID:UIS2025/2 DESCRIPTION:Title: Generalized Chiral Potts Models and Hyperbolic Monopoles from Chern -Simons Theories (Part1)\nby Masahito Yamazaki (Tokyo) as part of Nago ya IAR workshop on Unification of Integrable Systems\n\nLecture held in Sa kata-Hirata Hall\, Nagoya University.\n\nAbstract\nThe chiral Potts model is an exceptional integrable model whose spectral parameter lives on a sur face of genus greater than one. It was noticed later by Atiyah that the sa me spectral data appeared in the study of monopoles in the hyperbolic spac e. In this talk\, I will generalize the correspondence and explore its ori gin in holomorphic-topological Chern-Simons theories\, based on the recent paper arXiv:2502.17545 [hep-th] with Moosavian and Zhou.\n LOCATION:https://stable.researchseminars.org/talk/UIS2025/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Masashi Hamanaka (Nagoya) DTSTART:20251027T074500Z DTEND:20251027T084500Z DTSTAMP:20260404T095717Z UID:UIS2025/3 DESCRIPTION:Title: Towards Unification of Integrable Systems -- from ASD Yang-Mills vi ewpoints\nby Masashi Hamanaka (Nagoya) as part of Nagoya IAR workshop on Unification of Integrable Systems\n\nLecture held in Sakata-Hirata Hall \, Nagoya University.\n\nAbstract\nAnti-Self-Dual (ASD) Yang-Mills equatio ns have played important roles in quantum field theory\, four-dimensional geometry and integrable systems. The ASD Yang-Mills equations have two pot ential formalisms described by the J-matrix and the K-matrix. These equati ons by J and K are equations of motion of the 4-dimensional Wess-Zumino-Wi tten (4dWZW) model and the Leznov-Mukhtarov-Parkes (4dLMP) model\, respect ively. Both models can be space-time actions of N=2 open string theories i n (2+2) dimensions and hence solutions of the ASD Yang-Mills equations des crive classical physical objects in the N=2 open string theory. Furthermor e\, both 4dWZW and 4dLMP models can be obtained from six-dimensional Chern -Simons theory and hence can be one wing of the unification senario of int egrable systems (6dCS-->4dCS/ASDYM) described in scope of this workshop.\n \nIn this talk\, I review basic of ASD Yang-Mills equations and reduced eq uations in the framework of the Yang-Mills\, 4dWZW and 4dLMP models and gi ve soliton solutions of them with resonance processes clarifying differenc e with the classification theory of KP solitons by Yuji Kodama et al. Fina lly we discuss perspectives of the unification of integrable systems in th e split signature\, in noncommutative settings\, and in homotopy algebra f ormulations. (I note that Xianghang Zhang is developing a homotopy algebra formutation of string field theory action of the N=2 open string theory [ arXiv:2506.21247].)\n\nThis talk is partly based on collabolation with Sha n-chi Huang\, Hiroaki Kanno (Nagoya) and Shangshuai li (Ningbo) and Da-Jun Zhang (Shanghai): arXiv:2408.16554\, arXiv:2501.08250 arXiv:2212.11800 an d forthcoming papers.\n LOCATION:https://stable.researchseminars.org/talk/UIS2025/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Masahito Yamazaki (Tokyo) DTSTART:20251028T020000Z DTEND:20251028T030000Z DTSTAMP:20260404T095717Z UID:UIS2025/4 DESCRIPTION:Title: Generalized Chiral Potts Models and Hyperbolic Monopoles from Chern -Simons Theories (Part2)\nby Masahito Yamazaki (Tokyo) as part of Nago ya IAR workshop on Unification of Integrable Systems\n\nLecture held in Sa kata-Hirata Hall\, Nagoya University.\n\nAbstract\nThe chiral Potts model is an exceptional integrable model whose spectral parameter lives on a sur face of genus greater than one. It was noticed later by Atiyah that the sa me spectral data appeared in the study of monopoles in the hyperbolic spac e. In this talk\, I will generalize the correspondence and explore its ori gin in holomorphic-topological Chern-Simons theories\, based on the recent paper arXiv:2502.17545 [hep-th] with Moosavian and Zhou.\n LOCATION:https://stable.researchseminars.org/talk/UIS2025/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Benoit Vicedo (York) DTSTART:20251028T043000Z DTEND:20251028T060000Z DTSTAMP:20260404T095717Z UID:UIS2025/5 DESCRIPTION:Title: Lax integrability and holomorphic-topological gauge theory (Lecture 2)\nby Benoit Vicedo (York) as part of Nagoya IAR workshop on Unifica tion of Integrable Systems\n\nLecture held in Sakata-Hirata Hall\, Nagoya University.\n\nAbstract\nThe Lax formalism provides a powerful and unifyin g framework for describing classical integrable field theories in various spacetime dimensions. Its central object\, the Lax matrix\, depends on the spacetime coordinates and meromorphically on an auxiliary complex variabl e known as the spectral parameter.\n\n\n\nIn a series of recent seminal wo rks\, Costello\, Witten and Yamazaki have shown that the Lax formalism adm its a natural and elegant geometric origin in higher-dimensional holomorph ic-topological gauge theory. In this setting\, the spectral parameter is i ncorporated into the spacetime geometry and the Lax matrix arises as a spe cific component of the gauge field.\n\n\n\nIn these lectures I will give a n introduction to this connection between the Lax formalism and holomorphi c-topological gauge theories.\n\n\n\nLecture 1 - (1d IFTs) Lax pairs encod e the integrable structure of finite-dimensional integrable systems\, i.e. 1-dimensional integrable field theories\, such as the closed Toda chain o r the Gaudin model on a product of coadjoint orbits. After reviewing this formalism\, I will explain how the framework of spectral parameter depende nt Lax pairs naturally emerges from 3-dimensional holomorphic-topological BF theory.\n\n\n\nLecture 2 - (2d IFTs) Lax connections are an affine gene ralisation of Lax pairs which encode the integrable structure of 2-dimensi onal integrable field theories. I will review their deep connection to aff ine Gaudin models in the Hamiltonian formalism and explain how 4-dimension al holomorphic-topological Chern-Simons theory captures the same structure from a Lagrangian perspective.\n\n\n\nLecture 3 - (≥ 3d IFTs) In 3 dime nsions and above there is no general\, universally accepted definition of integrability. I will explain how the framework of holomorphic-topological gauge theories in 5-dimensions and above can be used as a guiding princip le for formulating appropriate higher-dimensional analogues of Lax integra bility. In particular\, I will introduce 5-dimensional holomorphic-topolog ical 2-Chern-Simons theory as a potential higher gauge-theoretic framework for describing 3-dimensional integrable field theories.\n LOCATION:https://stable.researchseminars.org/talk/UIS2025/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Kentaroh Yoshida (Saitama) DTSTART:20251028T063000Z DTEND:20251028T073000Z DTSTAMP:20260404T095717Z UID:UIS2025/6 DESCRIPTION:Title: The Courant-Hilbert construction in 4D Chern-Simons theory (Part 1) \nby Kentaroh Yoshida (Saitama) as part of Nagoya IAR workshop on Unif ication of Integrable Systems\n\nLecture held in Sakata-Hirata Hall\, Nago ya University.\n\nAbstract\nRecently\, the method developed by Courant and Hilbert (CH) has been shown to be able to generally describe various inte grable deformations of the 2D principal chiral model\, including the TTbar deformation and the root TTbar deformation. We show how this CH method ca n be described in 4D Chern-Simons (4D CS) theory. In particular\, for defo rmations with a dimensionful parameter such as the TTbar deformation\, a c orrection term\, the trace of the energy-momentum tensor\, must be added t o the original 4D CS theory. This correction term is consistent with the r esult shown by Sakamoto-Tateo-Yamazaki (2509.12303 [hep-th]) for the TTbar deformation and is generalized by the CH method.\n\nThis talk is based on the collaboration 2509.22080 [hep-th] with Osamu Fukushima (RIKEN iTHEMS) and Takaki Matsumoto (Seikei University).\n\nIn the first part\, we intro duce some basics of the TTbar deformation and the root TTbar deformation\, then we describe the CH construction of integrable deformations of the 2D principal chiral model.\n\nIn the second part\, we show how this CH metho d can be described in 4D CS theory.\n LOCATION:https://stable.researchseminars.org/talk/UIS2025/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Benoit Vicedo (York) DTSTART:20251029T043000Z DTEND:20251029T060000Z DTSTAMP:20260404T095717Z UID:UIS2025/7 DESCRIPTION:Title: Lax integrability and holomorphic-topological gauge theory (Lecture 3)\nby Benoit Vicedo (York) as part of Nagoya IAR workshop on Unifica tion of Integrable Systems\n\nLecture held in Sakata-Hirata Hall\, Nagoya University.\n\nAbstract\nThe Lax formalism provides a powerful and unifyin g framework for describing classical integrable field theories in various spacetime dimensions. Its central object\, the Lax matrix\, depends on the spacetime coordinates and meromorphically on an auxiliary complex variabl e known as the spectral parameter.\n\n\n\nIn a series of recent seminal wo rks\, Costello\, Witten and Yamazaki have shown that the Lax formalism adm its a natural and elegant geometric origin in higher-dimensional holomorph ic-topological gauge theory. In this setting\, the spectral parameter is i ncorporated into the spacetime geometry and the Lax matrix arises as a spe cific component of the gauge field.\n\n\n\nIn these lectures I will give a n introduction to this connection between the Lax formalism and holomorphi c-topological gauge theories.\n\n\n\nLecture 1 - (1d IFTs) Lax pairs encod e the integrable structure of finite-dimensional integrable systems\, i.e. 1-dimensional integrable field theories\, such as the closed Toda chain o r the Gaudin model on a product of coadjoint orbits. After reviewing this formalism\, I will explain how the framework of spectral parameter depende nt Lax pairs naturally emerges from 3-dimensional holomorphic-topological BF theory.\n\n\n\nLecture 2 - (2d IFTs) Lax connections are an affine gene ralisation of Lax pairs which encode the integrable structure of 2-dimensi onal integrable field theories. I will review their deep connection to aff ine Gaudin models in the Hamiltonian formalism and explain how 4-dimension al holomorphic-topological Chern-Simons theory captures the same structure from a Lagrangian perspective.\n\n\n\nLecture 3 - (≥ 3d IFTs) In 3 dime nsions and above there is no general\, universally accepted definition of integrability. I will explain how the framework of holomorphic-topological gauge theories in 5-dimensions and above can be used as a guiding princip le for formulating appropriate higher-dimensional analogues of Lax integra bility. In particular\, I will introduce 5-dimensional holomorphic-topolog ical 2-Chern-Simons theory as a potential higher gauge-theoretic framework for describing 3-dimensional integrable field theories.\n LOCATION:https://stable.researchseminars.org/talk/UIS2025/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Kentaroh Yoshida (Saitama) DTSTART:20251029T063000Z DTEND:20251029T073000Z DTSTAMP:20260404T095717Z UID:UIS2025/8 DESCRIPTION:Title: The Courant-Hilbert construction in 4D Chern-Simons theory (Part 2) \nby Kentaroh Yoshida (Saitama) as part of Nagoya IAR workshop on Unif ication of Integrable Systems\n\nLecture held in Sakata-Hirata Hall\, Nago ya University.\n\nAbstract\nRecently\, the method developed by Courant and Hilbert (CH) has been shown to be able to generally describe various inte grable deformations of the 2D principal chiral model\, including the TTbar deformation and the root TTbar deformation. We show how this CH method ca n be described in 4D Chern-Simons (4D CS) theory. In particular\, for defo rmations with a dimensionful parameter such as the TTbar deformation\, a c orrection term\, the trace of the energy-momentum tensor\, must be added t o the original 4D CS theory. This correction term is consistent with the r esult shown by Sakamoto-Tateo-Yamazaki (2509.12303 [hep-th]) for the TTbar deformation and is generalized by the CH method.\n\nThis talk is based on the collaboration 2509.22080 [hep-th] with Osamu Fukushima (RIKEN iTHEMS) and Takaki Matsumoto (Seikei University).\n\nIn the first part\, we intro duce some basics of the TTbar deformation and the root TTbar deformation\, then we describe the CH construction of integrable deformations of the 2D principal chiral model.\n\nIn the second part\, we show how this CH metho d can be described in 4D CS theory.\n LOCATION:https://stable.researchseminars.org/talk/UIS2025/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Hiroaki Matsunaga (Osaka) DTSTART:20251029T073000Z DTEND:20251029T080000Z DTSTAMP:20260404T095717Z UID:UIS2025/9 DESCRIPTION:Title: Homotopy algebraic approach to Lagrangian multiform\nby Hiroaki Matsunaga (Osaka) as part of Nagoya IAR workshop on Unification of Integr able Systems\n\nLecture held in Sakata-Hirata Hall\, Nagoya University.\n\ nAbstract\nLagrangian’s homotopy algebra may provide an alternative way to perform field-theoretical computations.\n\nIn this talk\, I study a hom otopy algebraic description of Lagrangian multiform theory and present tha t some generating Lagrangians in Lagrangian multiform theory can be writte n into the WZW-like form\, which appears in the formulation of superstring field theory.\n\nThis WZW-like action includes a tuple of L_infty algebra s\, and a modified classical Yang-Baxter equation of integrable models app ears in the L_infty relations manifestly.\n\nThis talk is partly based on discussion in Asahipen-meeting (on going work).\n LOCATION:https://stable.researchseminars.org/talk/UIS2025/9/ END:VEVENT END:VCALENDAR