[Turkmath:9713] Bob Oliver'in ziyareti

[Ergun Yalcin]

Degerli liste uyeleri,

Paris 13 Universitesi'nden Bob Oliver 14-24 Nisan tarihleri
arasinda Bilkent Universitesi'nde misafirimiz olacaktir. Bu 
ziyaret sirasinda asagida detaylari verilen iki konusmayi
yapacaktir. Butun ilgilenenleri bekleriz.

Saygilarimla,
Ergun Yalcin
  


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BILKENT GENERAL SEMINAR

Title:  Local structure of groups and of their classifying spaces

Speaker: Bob Oliver (Université PARIS 13)

Date: April 16, 2014 Wednesday 15:40-16:30 

Place: Math Department Seminar Room
 
Abstract: This will be a survey talk on the close relationship between
the local structure of a finite group or compact Lie group and that of its
classifying space.  By the ``p-local structure'' of a group G, for a
prime p, is meant the structure of a Sylow p-subgroup S of G (a
maximal p-toral subgroup if G is compact Lie), together with all
G-conjugacy relations between elements and subgroups of S.  By the
p-local structure of the classifying space BG is meant the structure
(homotopy properties) of the p-completion of BG.

For example, by a conjecture of Martino and Priddy, now a theorem, two
finite groups G and H have equivalent p-local structures if and only if
the p-completions of BG and BH are homotopy equivalent. This (the
``if'' part of the statement) was used, in joint work with Broto and
M{\o}ller, to prove a general theorem about local equivalences between
finite Lie groups --- a result for which no purely algebraic proof is
known.

As another example, these ideas have allowed us to extend the family of
p-completed classifying spaces of (finite or compact Lie) groups to a much
larger family of spaces which have many of the same very nice homotopy
theoretic properties.

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BILKENT ALGEBRAIC TOPOLOGY SEMINAR--10

Title: Reduced fusion systems over small 2-groups

Speaker: Bob Oliver (Université PARIS 13)

Date: April 21, 2014 Monday 13:40-15:00 

Place: Math Department Seminar Room

Abstract: The sectional rank of a finite p-group is the largest rank of any 
abelian subquotient. The sectional p-rank of a finite group is the sectional rank 
of its Sylow p-subgroups.

I will describe a result listing all reduced, indecomposable fusion systems 
over 2-groups of sectional rank at most four.  This is motivated 
by a theorem of Gorenstein and Harada, where they listed all finite 
simple groups of sectional 2-rank at most four. The new result contains no 
surprises:  the fusion systems in question are all those of simple groups 
on the Gorenstein-Harada list.  But the method of proof seems very 
different, since it is based on studying the different types of essential 
subgroups which can occur, rather than the centralizers of involutions.  
This also leads to a different way of organizing the final result, which 
I hope will be of interest.
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