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X-FROM-URL:https://eom.sdu.dk/events/ical/88f0fcd3-7793-46d5-9a1a-9c869b63
 c121
X-WR-CALNAME:QM Research Seminar: Fusion categories as (quantum) symmetrie
 s: stability conditions and Morita duality
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DTSTART:20261028T030000
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DESCRIPTION:[b]Speaker: Edmund Heng[/b] (Institut des Hautes Études Scient
 ifiques) [nl][nl]\n[b]Abstract:[/b][nl]\nClassically\, finite symmetries 
 are captured by the action of a finite group. Moving to the quantum world
 \, one has to allow for (possibly non-invertible) quantum symmetries — th
 ese are instead captured by the action of a more general algebraic struct
 ure\, known as a fusion category. Such quantum symmetries are actually ub
 iquitous in mathematics\; for example\, given a category with an action o
 f a finite group G (e.g. rep(Q)\, Coh(X) etc.)\, its G-equivariant catego
 ry has instead the action of the category of representations rep(G)\, whe
 re rep(G) has the structure of a fusion category (and is not just a group
  when G is non-abelian).  \nThe aim of this talk is to introduce fusion c
 ategories and discuss their role as “quantum symmetries” in relation to B
 ridgeland’s stability conditions. We first introduce a generalised notion
  replacing “G-invariant stability conditions” in the setting of a triangu
 lated category equipped an action of a fusion category C\, which we will 
 “C-equivariant stability conditions”. The first result is that these stab
 ility conditions form a closed submanifold of the stability manifold\, ju
 st as the G-invariant stability conditions do. Moreover\, given a triangu
 lated D with a G-action\, so that its G-equivariant category D^G has a re
 p(G)-action\, we will see the following (Morita) duality result for stabi
 lity conditions: the complex manifold of G-invariant stability conditions
  (associated to D) is homeomorphic to the complex manifold of rep(G)-equi
 variant stability conditions (associated to D^G).[nl]\nIf time allows\, I
  will discuss other more “exotic” actions of fusion categories on triangu
 lated categories\, and possibly its relation to Coxeter theory.[nl]\nThis
  is part of joint work with Hannah Dell and Anthony Licata. \n[nl]\n[nl]
DTEND:20240403T140000Z
DTSTAMP:20260602T163402Z
DTSTART:20240403T130000Z
LOCATION:Syddansk Universitet\, Campusvej 55\, 5230\, Odense M
SEQUENCE:0
SUMMARY:QM Research Seminar: Fusion categories as (quantum) symmetries: st
 ability conditions and Morita duality
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