BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Benoit Vicedo (York) DTSTART:20251029T043000Z DTEND:20251029T060000Z DTSTAMP:20260423T011049Z 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 END:VCALENDAR