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SUMMARY:Tim Logvinenko (Cardiff)
DTSTART:20200519T130000Z
DTEND:20200519T140000Z
DTSTAMP:20260423T005800Z
UID:notts_ag/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/notts_ag/12/
 ">Skein-triangulated representations of generalised braids</a>\nby Tim Log
 vinenko (Cardiff) as part of Online Nottingham algebraic geometry seminar\
 n\n\nAbstract\nOrdinary braid group $\\mathrm{Br}_n$ is a well-known algeb
 raic structure which encodes configurations of $n$ non-touching strands ("
 braids") up to continuous transformations ("isotopies"). A classical resul
 t of Khovanov and Thomas states that there is a natural categorical action
  of $\\mathrm{Br}_n$ on the derived category of the cotangent bundle of th
 e variety of complete flags in $\\mathbb{C}^n$. In this talk\, I will intr
 oduce a new structure: the category $\\mathrm{GBr}_n$ of generalised braid
 s. These are the braids whose strands are allowed to touch in a certain wa
 y. They have multiple endpoint configurations and can be non-invertible\, 
 thus forming a category rather than a group. In the context of triangulate
 d categories\, it is natural to impose certain relations which result in t
 he notion of a skein-triangulated representation of $\\mathrm{GBr}_n$. A d
 ecade-old conjecture states that there a skein-triangulated action of $\\m
 athrm{GBr}_n$ on the cotangent bundles of the varieties of full and partia
 l flags in $\\mathbb{C}^n$. We prove this conjecture for $n = 3$. We also 
 show that any categorical action of $\\mathrm{Br}_n$ can be lifted to a sk
 ein-triangulated action of $\\mathrm{GBr}_n$\, which behaves like a catego
 rical nil Hecke algebra. This is a joint work with Rina Anno and Lorenzo D
 e Biase.\n
LOCATION:https://researchseminars.org/talk/notts_ag/12/
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