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 M3//EN
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BEGIN:VEVENT
DTSTAMP:20250321T121948Z
DTSTART:20250325T140000Z
DTEND:20250325T150000Z
SUMMARY:Algebra seminar - Marina Anagnostopoulou-Merkouri
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}z1qc-m7em1o
 fj-er0ygk
DESCRIPTION:Title: The regularity number of a finite group\n\nAbstract: L
 et $G$ be a transitive permutation group on a finite set $\\Omega$ with 
 point stabiliser $H$. Recall that a base for $G$ is a subset of $\\Omega
 $ whose pointwise stabiliser in $G$ is trivial. The minimal size of a ba
 se is called the base size of $G$\, denoted b(G)\, and this classical in
 variant has been widely studied for many years\, finding many applicatio
 ns.\n\nObserve that $b(G)$ coincides with the smallest positive integer 
 $k$ such that $G$ has a regular orbit on the Cartesian product $(G/H)^k$
 . As a natural generalisation\, we can consider the minimal number $r$ s
 uch that $G$ has a regular orbit on $(G/H_1) \\times \\cdots \\times (G/
 H_r)$ for any core-free subgroups $H_1\, \\ldots\, H_r$ of $G$. We call 
 this invariant the regularity number of $G$.\n\nIn this talk\, we will e
 xplain how a combination of probabilistic\, combinatorial and computatio
 nal methods can be used to study the regularity number of almost simple 
 groups\, as well as several other related problems. In particular\, we w
 ill report on some recent progress towards extensions of well studied ba
 se size conjectures of Cameron and Vdovin. This is joint work with Tim B
 urness.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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