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SUMMARY:Kamilla Rekvenyi (Imperial)
DTSTART:20230314T140000Z
DTEND:20230314T150000Z
DTSTAMP:20260421T153818Z
UID:UEAPS/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UEAPS/4/">Th
 e Orbital Diameter of Primitive Permutation Groups</a>\nby Kamilla Rekveny
 i (Imperial) as part of ANTLR seminar\n\nLecture held in NEWSCI 0.06.\n\nA
 bstract\nLet G be a group acting transitively on a finite set Ω. Then G a
 cts on ΩxΩ component wise. Define the orbitals to be the orbits of G on 
 ΩxΩ. The diagonal orbital is the orbital of the form ∆ = {(α\, α)|α
  ∈ Ω}. The others are called non-diagonal orbitals. Let Γ be a non-di
 agonal orbital. Define an orbital graph to be the non-directed graph with 
 vertex set Ω and edge set (α\,β)∈ Γ with α\,β∈ Ω. If the action
  of G on Ω is primitive\, then all non-diagonal orbital graphs are connec
 ted. The orbital diameter of a primitive permutation group is the supremum
  of the diameters of its non-diagonal orbital graphs.\n\nThere has been a 
 lot of interest in finding bounds on the orbital diameter of primitive per
 mutation groups. In my talk I will outline some important background infor
 mation and the progress made towards finding explicit bounds on the orbita
 l diameter. In particular\, I will discuss some results on the orbital dia
 meter of the groups of simple diagonal type and their connection to the co
 vering number of finite simple groups. I will also discuss some results fo
 r affine groups\, which provides a nice connection to the representation t
 heory of quasisimple groups.\n
LOCATION:https://researchseminars.org/talk/UEAPS/4/
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