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PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
 M3//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20251007T143409Z
DTSTART:20251028T140000Z
DTEND:20251028T150000Z
SUMMARY:Heilbronn Algebra Seminar - Tim Burness
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}zyy-mggnif5
 5-213mm0
DESCRIPTION:Title: Simple groups\, nilpotent subgroups and their intersec
 tions\n \nAbstract:\n \nLet G be a finite group\, let p be a prime and l
 et H be a Sylow p-subgroup. Problems concerning the intersections of Syl
 ow subgroups have been studied for many decades. For example\, a theorem
  of Ito from 1958 shows that if G has odd order\, then H \\cap H^x = O_p
 (G) for some element x in G\, where O_p(G) is the intersection of all th
 e Sylow p-subgroups of G. And for an arbitrary finite group G\, Zenkov (
 1996) uses CFSG to show that H \\cap H^x \\cap H^y = O_p(G) for some x\,
 y in G. In the special case where G is a (non-abelian) simple group\, th
 e main result is due to Mazurov and Zenkov (1996)\, who showed that H \\
 cap H^x = 1 for some x in G. Their proof of the latter result uses earli
 er work from the 1980s on defect groups of p-blocks for simple groups of
  Lie type.\n \nIn this talk\, I will present a probabilistic approach to
  study the intersections of randomly chosen Sylow p-subgroups. For non-a
 lternating simple groups\, we will use this method to verify an interest
 ing conjecture of Lisi and Sabatini (2025) on “synchronised intersection
 s" of Sylow subgroups. Our method yields a new proof of the Mazurov-Zenk
 ov theorem for these groups\, and we are also able to complete the proof
  of a strong form of a conjecture of Vdovin from 2002 on intersections o
 f nilpotent subgroups of simple groups: if G is simple and H\,K are nilp
 otent subgroups\, then H \\cap K^x = 1 for some element x in G. Along th
 e way\, we establish new asymptotic results on the probability that two 
 random Sylow p-subgroups in a simple group of Lie type have trivial inte
 rsection\, complementing recent work of Diaconis et al. (2025) and Eberh
 ard (2025) on symmetric and alternating groups.\nThis is joint work with
  Hongyi Huang (SUSTech\, China).
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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