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SUMMARY:Mikhail Gorsky (Laboratoire de Mathématiques de Versailles\, Fran
 ce)
DTSTART:20220707T110000Z
DTEND:20220707T120000Z
DTSTAMP:20260423T041526Z
UID:LAGOON/74
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LAGOON/74/">
 Cluster structures on braid varieties</a>\nby Mikhail Gorsky (Laboratoire 
 de Mathématiques de Versailles\, France) as part of Longitudinal Algebra 
 and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nA braid variety i
 s a certain affine algebraic variety associated with a \nsimply-connected 
 simple algebraic group G and a positive braid of the \ncorresponding type.
  These varieties generalise open Richardson varieties \nand appear in the 
 context of symplectic topology and in the study of \nlink invariants such 
 as HOMFLY-PT polynomials and Khovanov-Rozansky \nhomology.\nIn this talk\,
  I will give a proof of the existence of cluster \nA-structures and cluste
 r Poisson structures on any braid variety. I will \nsketch an explicit con
 struction of cluster seeds involving the \ndiagrammatic calculus of weaves
  and a tropicalization of Lustig's \ncoordinates. These cluster algebras a
 re local acyclic and equal their \nupper cluster algebras. The main result
  also proves the conjecture of B. \nLeclerc on the existence of cluster al
 gebra structures on the coordinate \nrings of open Richardson varieties in
  simply laced types. The talk is \nbased on joint work with Roger Casals\,
  Eugene Gorsky\, Ian Le\, Linhui \nShen\, and José Simental.\n\nMeeting L
 ink\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQ
 Wk3dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/74/
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