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SUMMARY:Skein-triangulated representations of generalised braids [MPIM]
DTSTART:20260709T130000Z
DTEND:20260709T140000Z
DTSTAMP:20260703T170600Z
UID:indico-event-1469@math-events.uni-bonn.de
DESCRIPTION:Speakers: Timothy Logvinenko (Cardiff University/MPIM)\n\nMPI-
 Oberseminar\nThere are many examples where the braid group Br_n acts on th
 e derived category of an algebraic variety: the minimal resolutions of Kle
 inian singularities\, the cotangent bundles of flag varieties\, etc. I wil
 l describe a long-running project with Rina Anno (Kansas) where we introdu
 ce a new structure: the category GBr_n of generalised braids. These are th
 e braids whose strands are allowed to touch in a certain way. We consider 
 these strands embedded in a ribbon graph\, and allow ribbon twists.\nFor t
 riangulated categories\, it is natural to impose certain relations which r
 esult in the notion of a skein-triangulated representation of GBr_n. These
  relations categorify the polynomial sl_n-web calculus used in the constru
 ction of Khovanov-Rozansky homology. We give two examples of skein-triangu
 lated actions of GBr_n: on the cotangent bundles of flag varieties and on 
 categorical nil-Hecke algebras. The latter example shows that any categori
 cal action of Br_n can be lifted to a skein-triangulated action of GBr_n\,
  generalising a result of Ed Segal that all autoequivalences are spherical
  twists.\n\nhttps://math-events.uni-bonn.de/event/1469/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1469/
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