[Turkmath:3349] Bilkent Cebir Semineri 05.11.2018

[Bilkent Mathematics]

Değerli liste üyeleri, 

 

Bilkent Matematik Bölümü Cebir Seminerleri kapsamında 5 Kasım'da Laurence
Barker konuşmacı olacaktır. 

 

 

Laurence Barker (Bilkent Üniversitesi) 

 

"An introduction to fusion systems, Alperin's Weight Conjecture,
Linckelmann's Gluing Conjecture, part 1" 

 

Özet: One aim of p-local finite group theory, arguably, is to get rid of the
particular arbitrary famous finite group G and to retain only general
p-local structure, perhaps partially expressed though categories whose
objects are to be finite p-groups. In plain group theory, we consider the
$p$-subgroups and the transports between them effected by conjugations.
Sylow's Theorem allows us to localize, reducing to a consideration of
morphisms between subgroups of a fixed Sylow p-subgroup. In block theory,
the p-subgroups are replaced by the more general notion of a Brauer pair.
Applying an analogue of Sylow's Theorem, the role of the Sylow p-subgroups
is performed by p-subgroups called the defect groups. We can reduce to a
category called the fusion system, whose objects are the subgroups of the
defect group.

Alperin's Fusion Theorem motivates a confinement of attention to only those
objects that are called centric.

 

But the invariants appearing in Alperin's Conjecture are not invariants of
the fusion system. After Kuelshammer and Puig, we capture the desired local
information by assigning, to each centric object, a twist of the
automorphism group over the unit group of the coefficient field, we mean, a
central extension that is well-defined up to canonical isomorphism. Near the
end of part 1 or the start of part 2, we shall illustrate the centric fusion
system and its twists by means of an illuminating example, the Sylow-defect
p-blocks of SL(3, p), where the prime p is congruent to 1 modulo 3.

 

 

Tarih: 5 Kasım 2018 Pazartesi, 10:40-11:50

Bilkent Matematik Bölümü Seminer Odası SA - 141 Konuşma öncesinde
çay-kurabiye ikramı yapılacaktır. 

 

İlgilenen herkes davetlidir. 

 

Bilkent Üniversitesi Matematik Bölümü

https://twitter.com/Bilkent_math

 

 

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