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X-WR-CALNAME:QM Research Seminar: Homological Algebra and Integrability
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TZID:Europe/Copenhagen
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DTSTAMP:20260513T130431Z
DTSTART:20261028T030000
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DESCRIPTION:[b]Speaker: Ryan Cullinan [/b](​University of York).\n\n[b]Abs
 tract: [/b]\nIntegrable systems provide a pragmatic point in the landscap
 e of physical theories. Such systems are characterised by their solvabili
 ty\, which is usually underpinned by the possession of an infinite-dimens
 ional symmetry group\, the existence of solitonic solutions\, or admittan
 ce of an algebro-geometric description of the system.\n\nGiven the abunda
 nce of models deemed ‘integrable’ in one of the aforementioned senses\, i
 t becomes essential to ask what universal characteristics these models sh
 are that enable their integrability. A systematic understanding of Lax in
 tegrability for integrable field theories in two dimensions was provided 
 by the introduction of a topological holomorphic theory in four dimension
 s called four-dimensional Chern-Simons theory\, which illuminates many of
  the superficially mysterious aspects of a system's integrability by desc
 ribing the data of a two-dimensional integrable field theory in the langu
 age of four-dimensional gauge theory.\n\nIn this talk\, we will describe 
 the refinements required to build on this paradigm by studying a topologi
 cal-holomorphic theory in five dimensions called five-dimensional 2-Chern
 -Simons. The aforementioned theory is a 2-categorical generalisation of i
 ts four-dimensional counterpart\, describing Lax integrable field theorie
 s in three dimensions via the medium of higher categorical gauge theory. 
 Bringing together results from homotopical and homological algebra\, Hodg
 e theory\, and the BV formalism\, we will outline the subtleties in defin
 ing the theory and in attempting to chart this new landscape of 'higher L
 ax integrable' theories.
DTEND:20260324T140000Z
DTSTAMP:20260513T130431Z
DTSTART:20260324T130000Z
LOCATION:Syddansk Universitet\, Campusvej 55\, 5230\, Odense M
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SUMMARY:QM Research Seminar: Homological Algebra and Integrability
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