BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Saebyeok Jeong (Rutgers U) DTSTART:20210608T070000Z DTEND:20210608T083000Z DTSTAMP:20260404T111006Z UID:SNUSTRING/1 DESCRIPTION:Title: Boundaries\, defects\, and quantization\nby Saebyeok Jeong (R utgers U) as part of SNU String Seminar\n\n\nAbstract\nAn interesting aspe ct of four-dimensional N=2 supersymmetric field theories is their correspo ndence with integrable systems. At the example of class S theories and Hit chin integrable systems\, I will explain how half-BPS defects in gauge the ory can be utilized in the quantization problem. More specifically\, the v acuum expectation values and correlation functions of these defects are ex actly computed by localization\, and analytic constraints make them obey c ertain differential equations in coupling parameters. These equations and solutions are interpreted geometrically in the Hitchin moduli space side\, yielding various implications on the quantization problem. I will also di scuss how these results can be reformulated in the point of view of the tw o-dimensional sigma model with the Hitchin target space\, connecting the s tory to that of the N=4 theory of Kapustin-Witten.\n LOCATION:https://stable.researchseminars.org/talk/SNUSTRING/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Saebyeok Jeong (Rutgers U) DTSTART:20220802T050000Z DTEND:20220802T070000Z DTSTAMP:20260404T111006Z UID:SNUSTRING/2 DESCRIPTION:Title: Fusion of surface defects\, Hecke operator\, and quantum Lax equa tion\nby Saebyeok Jeong (Rutgers U) as part of SNU String Seminar\n\n\ nAbstract\nI will consider a correlation function of two half-BPS surface defects in 4d N=2 gauge theory of class S\, which have different 6d origin s. I will explain their meaning after the reduction to the sigma model on a corner with the Hitchin moduli space target. By localization computation \, we confirm that the introduction of the second surface defect induces a n action on the parameter space of the first surface defect\, which is sho wn to be that of the Hecke operator on the conformal block of the vertex a lgebra at the junction of the corner. Furthermore\, the correlation functi on is shown to satisfy the 'quantum' Lax equation\, leading to all the mut ually commuting quantum Hamiltonian realized as differential operators act ing on the vev of the first surface defect.\n LOCATION:https://stable.researchseminars.org/talk/SNUSTRING/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Satoshi Yamaguchi (Osaka University) DTSTART:20230130T050000Z DTEND:20230130T070000Z DTSTAMP:20260404T111006Z UID:SNUSTRING/3 DESCRIPTION:Title: Non-invertible symmetries on the lattice (1/2)\nby Satoshi Ya maguchi (Osaka University) as part of SNU String Seminar\n\n\nAbstract\nRe cently\, the study of generalized symmetries and their applications has be en rapidly developing. In particular\, examples of a class of generalized symmetry called "non-invertible symmetries" have been found in four dimens ions. The key idea in this development is the "topological defects." An ap proach to such generalized symmetry and topological defects is through th e lattice theory approach developed by Aasen\, Mong\, and Fendley. In this lecture\, I will explain this AMF approach and the generalization to four dimensions done by Koide\, Nagoya\, and myself. I will start with one-dim ensional systems and explain the relation between classical statistical m echanics and quantum mechanics as well as operators and defects. Then\, I will turn to two dimensions and explain the Kramerse-Wannier duality and i ts manifestation by non-invertible topological defects. Finally\, I will e xplain our own work on the topological defects in the four dimensional Z2 lattice gauge theory.\n LOCATION:https://stable.researchseminars.org/talk/SNUSTRING/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Satoshi Yamaguchi (Osaka University) DTSTART:20230131T050000Z DTEND:20230131T070000Z DTSTAMP:20260404T111006Z UID:SNUSTRING/4 DESCRIPTION:Title: Non-invertible symmetries on the lattice (2/2)\nby Satoshi Ya maguchi (Osaka University) as part of SNU String Seminar\n\n\nAbstract\nRe cently\, the study of generalized symmetries and their applications has be en rapidly developing. In particular\, examples of a class of generalized symmetry called "non-invertible symmetries" have been found in four dimens ions. The key idea in this development is the "topological defects." An ap proach to such generalized symmetry and topological defects is through th e lattice theory approach developed by Aasen\, Mong\, and Fendley. In this lecture\, I will explain this AMF approach and the generalization to four dimensions done by Koide\, Nagoya\, and myself. I will start with one-dim ensional systems and explain the relation between classical statistical m echanics and quantum mechanics as well as operators and defects. Then\, I will turn to two dimensions and explain the Kramerse-Wannier duality and i ts manifestation by non-invertible topological defects. Finally\, I will e xplain our own work on the topological defects in the four dimensional Z2 lattice gauge theory.\n LOCATION:https://stable.researchseminars.org/talk/SNUSTRING/4/ END:VEVENT END:VCALENDAR