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:20260422T215001Z 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 Unification of Integrable Systems\n\nLecture held in Sakata-Hirata Hall\, Nagoya Univers ity.\n\nAbstract\nThe Lax formalism provides a powerful and unifying frame work for describing classical integrable field theories in various spaceti me dimensions. Its central object\, the Lax matrix\, depends on the spacet ime coordinates and meromorphically on an auxiliary complex variable known as the spectral parameter.\n\n\n\nIn a series of recent seminal works\, C ostello\, Witten and Yamazaki have shown that the Lax formalism admits a n atural and elegant geometric origin in higher-dimensional holomorphic-topo logical gauge theory. In this setting\, the spectral parameter is incorpor ated into the spacetime geometry and the Lax matrix arises as a specific c omponent of the gauge field.\n\n\n\nIn these lectures I will give an intro duction to this connection between the Lax formalism and holomorphic-topol ogical gauge theories.\n\n\n\nLecture 1 - (1d IFTs) Lax pairs encode the i ntegrable structure of finite-dimensional integrable systems\, i.e. 1-dime nsional integrable field theories\, such as the closed Toda chain or the G audin model on a product of coadjoint orbits. After reviewing this formali sm\, I will explain how the framework of spectral parameter dependent Lax pairs naturally emerges from 3-dimensional holomorphic-topological BF theo ry.\n\n\n\nLecture 2 - (2d IFTs) Lax connections are an affine generalisat ion of Lax pairs which encode the integrable structure of 2-dimensional in tegrable field theories. I will review their deep connection to affine Gau din models in the Hamiltonian formalism and explain how 4-dimensional holo morphic-topological Chern-Simons theory captures the same structure from a Lagrangian perspective.\n\n\n\nLecture 3 - (≥ 3d IFTs) In 3 dimensions and above there is no general\, universally accepted definition of integra bility. I will explain how the framework of holomorphic-topological gauge theories in 5-dimensions and above can be used as a guiding principle for formulating appropriate higher-dimensional analogues of Lax integrability. In particular\, I will introduce 5-dimensional holomorphic-topological 2- Chern-Simons theory as a potential higher gauge-theoretic framework for de scribing 3-dimensional integrable field theories.\n LOCATION:https://researchseminars.org/talk/UIS2025/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Masahito Yamazaki (Tokyo) DTSTART:20251027T063000Z DTEND:20251027T073000Z DTSTAMP:20260422T215001Z UID:UIS2025/2 DESCRIPTION:Title: Generalized Chiral Potts Models and Hyperbolic Monopoles from Chern-Simons Theories (Part1)\nby Masahito Yamazaki (Tokyo) as part of Nagoya IAR workshop on Unification of Integrable Systems\n\nLecture held in Sakata-Hi rata Hall\, Nagoya University.\n\nAbstract\nThe chiral Potts model is an e xceptional integrable model whose spectral parameter lives on a surface of genus greater than one. It was noticed later by Atiyah that the same spec tral data appeared in the study of monopoles in the hyperbolic space. In t his talk\, I will generalize the correspondence and explore its origin in holomorphic-topological Chern-Simons theories\, based on the recent paper arXiv:2502.17545 [hep-th] with Moosavian and Zhou.\n LOCATION:https://researchseminars.org/talk/UIS2025/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Masashi Hamanaka (Nagoya) DTSTART:20251027T074500Z DTEND:20251027T084500Z DTSTAMP:20260422T215001Z UID:UIS2025/3 DESCRIPTION:Title: Towards Unification of Integrable Systems -- from ASD Yang-Mills viewpoint s\nby Masashi Hamanaka (Nagoya) as part of Nagoya IAR workshop on Unif ication of Integrable Systems\n\nLecture held in Sakata-Hirata Hall\, Nago ya University.\n\nAbstract\nAnti-Self-Dual (ASD) Yang-Mills equations have played important roles in quantum field theory\, four-dimensional geometr y and integrable systems. The ASD Yang-Mills equations have two potential formalisms described by the J-matrix and the K-matrix. These equations by J and K are equations of motion of the 4-dimensional Wess-Zumino-Witten (4 dWZW) model and the Leznov-Mukhtarov-Parkes (4dLMP) model\, respectively. Both models can be space-time actions of N=2 open string theories in (2+2) dimensions and hence solutions of the ASD Yang-Mills equations descrive c lassical physical objects in the N=2 open string theory. Furthermore\, bot h 4dWZW and 4dLMP models can be obtained from six-dimensional Chern-Simons theory and hence can be one wing of the unification senario of integrable systems (6dCS-->4dCS/ASDYM) described in scope of this workshop.\n\nIn th is talk\, I review basic of ASD Yang-Mills equations and reduced equations in the framework of the Yang-Mills\, 4dWZW and 4dLMP models and give soli ton solutions of them with resonance processes clarifying difference with the classification theory of KP solitons by Yuji Kodama et al. Finally we discuss perspectives of the unification of integrable systems in the split signature\, in noncommutative settings\, and in homotopy algebra formulat ions. (I note that Xianghang Zhang is developing a homotopy algebra formut ation of string field theory action of the N=2 open string theory [arXiv:2 506.21247].)\n\nThis talk is partly based on collabolation with Shan-chi H uang\, Hiroaki Kanno (Nagoya) and Shangshuai li (Ningbo) and Da-Jun Zhang (Shanghai): arXiv:2408.16554\, arXiv:2501.08250 arXiv:2212.11800 and forth coming papers.\n LOCATION:https://researchseminars.org/talk/UIS2025/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Masahito Yamazaki (Tokyo) DTSTART:20251028T020000Z DTEND:20251028T030000Z DTSTAMP:20260422T215001Z UID:UIS2025/4 DESCRIPTION:Title: Generalized Chiral Potts Models and Hyperbolic Monopoles from Chern-Simons Theories (Part2)\nby Masahito Yamazaki (Tokyo) as part of Nagoya IAR workshop on Unification of Integrable Systems\n\nLecture held in Sakata-Hi rata Hall\, Nagoya University.\n\nAbstract\nThe chiral Potts model is an e xceptional integrable model whose spectral parameter lives on a surface of genus greater than one. It was noticed later by Atiyah that the same spec tral data appeared in the study of monopoles in the hyperbolic space. In t his talk\, I will generalize the correspondence and explore its origin in holomorphic-topological Chern-Simons theories\, based on the recent paper arXiv:2502.17545 [hep-th] with Moosavian and Zhou.\n LOCATION:https://researchseminars.org/talk/UIS2025/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Benoit Vicedo (York) DTSTART:20251028T043000Z DTEND:20251028T060000Z DTSTAMP:20260422T215001Z 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 Unification of Integrable Systems\n\nLecture held in Sakata-Hirata Hall\, Nagoya Univers ity.\n\nAbstract\nThe Lax formalism provides a powerful and unifying frame work for describing classical integrable field theories in various spaceti me dimensions. Its central object\, the Lax matrix\, depends on the spacet ime coordinates and meromorphically on an auxiliary complex variable known as the spectral parameter.\n\n\n\nIn a series of recent seminal works\, C ostello\, Witten and Yamazaki have shown that the Lax formalism admits a n atural and elegant geometric origin in higher-dimensional holomorphic-topo logical gauge theory. In this setting\, the spectral parameter is incorpor ated into the spacetime geometry and the Lax matrix arises as a specific c omponent of the gauge field.\n\n\n\nIn these lectures I will give an intro duction to this connection between the Lax formalism and holomorphic-topol ogical gauge theories.\n\n\n\nLecture 1 - (1d IFTs) Lax pairs encode the i ntegrable structure of finite-dimensional integrable systems\, i.e. 1-dime nsional integrable field theories\, such as the closed Toda chain or the G audin model on a product of coadjoint orbits. After reviewing this formali sm\, I will explain how the framework of spectral parameter dependent Lax pairs naturally emerges from 3-dimensional holomorphic-topological BF theo ry.\n\n\n\nLecture 2 - (2d IFTs) Lax connections are an affine generalisat ion of Lax pairs which encode the integrable structure of 2-dimensional in tegrable field theories. I will review their deep connection to affine Gau din models in the Hamiltonian formalism and explain how 4-dimensional holo morphic-topological Chern-Simons theory captures the same structure from a Lagrangian perspective.\n\n\n\nLecture 3 - (≥ 3d IFTs) In 3 dimensions and above there is no general\, universally accepted definition of integra bility. I will explain how the framework of holomorphic-topological gauge theories in 5-dimensions and above can be used as a guiding principle for formulating appropriate higher-dimensional analogues of Lax integrability. In particular\, I will introduce 5-dimensional holomorphic-topological 2- Chern-Simons theory as a potential higher gauge-theoretic framework for de scribing 3-dimensional integrable field theories.\n LOCATION:https://researchseminars.org/talk/UIS2025/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Kentaroh Yoshida (Saitama) DTSTART:20251028T063000Z DTEND:20251028T073000Z DTSTAMP:20260422T215001Z UID:UIS2025/6 DESCRIPTION:Title: The Courant-Hilbert construction in 4D Chern-Simons theory (Part 1)\nb y Kentaroh Yoshida (Saitama) as part of Nagoya IAR workshop on Unification of Integrable Systems\n\nLecture held in Sakata-Hirata Hall\, Nagoya Univ ersity.\n\nAbstract\nRecently\, the method developed by Courant and Hilber t (CH) has been shown to be able to generally describe various integrable deformations of the 2D principal chiral model\, including the TTbar deform ation and the root TTbar deformation. We show how this CH method can be de scribed in 4D Chern-Simons (4D CS) theory. In particular\, for deformation s with a dimensionful parameter such as the TTbar deformation\, a correcti on term\, the trace of the energy-momentum tensor\, must be added to the o riginal 4D CS theory. This correction term is consistent with the result s hown by Sakamoto-Tateo-Yamazaki (2509.12303 [hep-th]) for the TTbar deform ation and is generalized by the CH method.\n\nThis talk is based on the co llaboration 2509.22080 [hep-th] with Osamu Fukushima (RIKEN iTHEMS) and Ta kaki Matsumoto (Seikei University).\n\nIn the first part\, we introduce so me basics of the TTbar deformation and the root TTbar deformation\, then w e describe the CH construction of integrable deformations of the 2D princi pal chiral model.\n\nIn the second part\, we show how this CH method can b e described in 4D CS theory.\n LOCATION:https://researchseminars.org/talk/UIS2025/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Benoit Vicedo (York) DTSTART:20251029T043000Z DTEND:20251029T060000Z DTSTAMP:20260422T215001Z 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 Unification of Integrable Systems\n\nLecture held in Sakata-Hirata Hall\, Nagoya Univers ity.\n\nAbstract\nThe Lax formalism provides a powerful and unifying frame work for describing classical integrable field theories in various spaceti me dimensions. Its central object\, the Lax matrix\, depends on the spacet ime coordinates and meromorphically on an auxiliary complex variable known as the spectral parameter.\n\n\n\nIn a series of recent seminal works\, C ostello\, Witten and Yamazaki have shown that the Lax formalism admits a n atural and elegant geometric origin in higher-dimensional holomorphic-topo logical gauge theory. In this setting\, the spectral parameter is incorpor ated into the spacetime geometry and the Lax matrix arises as a specific c omponent of the gauge field.\n\n\n\nIn these lectures I will give an intro duction to this connection between the Lax formalism and holomorphic-topol ogical gauge theories.\n\n\n\nLecture 1 - (1d IFTs) Lax pairs encode the i ntegrable structure of finite-dimensional integrable systems\, i.e. 1-dime nsional integrable field theories\, such as the closed Toda chain or the G audin model on a product of coadjoint orbits. After reviewing this formali sm\, I will explain how the framework of spectral parameter dependent Lax pairs naturally emerges from 3-dimensional holomorphic-topological BF theo ry.\n\n\n\nLecture 2 - (2d IFTs) Lax connections are an affine generalisat ion of Lax pairs which encode the integrable structure of 2-dimensional in tegrable field theories. I will review their deep connection to affine Gau din models in the Hamiltonian formalism and explain how 4-dimensional holo morphic-topological Chern-Simons theory captures the same structure from a Lagrangian perspective.\n\n\n\nLecture 3 - (≥ 3d IFTs) In 3 dimensions and above there is no general\, universally accepted definition of integra bility. I will explain how the framework of holomorphic-topological gauge theories in 5-dimensions and above can be used as a guiding principle for formulating appropriate higher-dimensional analogues of Lax integrability. In particular\, I will introduce 5-dimensional holomorphic-topological 2- Chern-Simons theory as a potential higher gauge-theoretic framework for de scribing 3-dimensional integrable field theories.\n LOCATION:https://researchseminars.org/talk/UIS2025/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Kentaroh Yoshida (Saitama) DTSTART:20251029T063000Z DTEND:20251029T073000Z DTSTAMP:20260422T215001Z UID:UIS2025/8 DESCRIPTION:Title: The Courant-Hilbert construction in 4D Chern-Simons theory (Part 2)\nb y Kentaroh Yoshida (Saitama) as part of Nagoya IAR workshop on Unification of Integrable Systems\n\nLecture held in Sakata-Hirata Hall\, Nagoya Univ ersity.\n\nAbstract\nRecently\, the method developed by Courant and Hilber t (CH) has been shown to be able to generally describe various integrable deformations of the 2D principal chiral model\, including the TTbar deform ation and the root TTbar deformation. We show how this CH method can be de scribed in 4D Chern-Simons (4D CS) theory. In particular\, for deformation s with a dimensionful parameter such as the TTbar deformation\, a correcti on term\, the trace of the energy-momentum tensor\, must be added to the o riginal 4D CS theory. This correction term is consistent with the result s hown by Sakamoto-Tateo-Yamazaki (2509.12303 [hep-th]) for the TTbar deform ation and is generalized by the CH method.\n\nThis talk is based on the co llaboration 2509.22080 [hep-th] with Osamu Fukushima (RIKEN iTHEMS) and Ta kaki Matsumoto (Seikei University).\n\nIn the first part\, we introduce so me basics of the TTbar deformation and the root TTbar deformation\, then w e describe the CH construction of integrable deformations of the 2D princi pal chiral model.\n\nIn the second part\, we show how this CH method can b e described in 4D CS theory.\n LOCATION:https://researchseminars.org/talk/UIS2025/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Hiroaki Matsunaga (Osaka) DTSTART:20251029T073000Z DTEND:20251029T080000Z DTSTAMP:20260422T215001Z UID:UIS2025/9 DESCRIPTION:Title: Homotopy algebraic approach to Lagrangian multiform\nby Hiroaki Matsun aga (Osaka) as part of Nagoya IAR workshop on Unification of Integrable Sy stems\n\nLecture held in Sakata-Hirata Hall\, Nagoya University.\n\nAbstra ct\nLagrangian’s homotopy algebra may provide an alternative way to perf orm field-theoretical computations.\n\nIn this talk\, I study a homotopy a lgebraic description of Lagrangian multiform theory and present that some generating Lagrangians in Lagrangian multiform theory can be written 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 algebras\, and a modified classical Yang-Baxter equation of integrable models appears in the L_infty relations manifestly.\n\nThis talk is partly based on discuss ion in Asahipen-meeting (on going work).\n LOCATION:https://researchseminars.org/talk/UIS2025/9/ END:VEVENT END:VCALENDAR