[Turkmath:3447] Bilkent Cebir Semineri - Sune Precht Reeh - 3.12.2018

[Bilkent Mathematics]

Değerli liste üyeleri, 

Bilkent Matematik Bölümü Cebir Seminerleri kapsamında 3 Aralık'ta Sune
Precht Reeh konuşmacı olacaktır. 


Sune Precht Reeh (Universitat Autònoma de Barcelona)


"Partial categories -- a proposal for constructing orbit categories of
saturated fusion systems"
 
Özet: Given a finite group G the orbit category of G consists of all
transitive G-sets and equivariant maps between them. Aside from algebra the
orbit category has also proved very useful in topology for describing
G-equivariant homotopy theory. For a saturated fusion system/p-local finite
group F with Sylow subgroup S the existing constructions of an orbit
category of F only makes sense for subgroups of S that are "sufficiently
large". In this talk I will propose a construction of an orbit category for
F that works for all subgroups of S, but the result will be a "partial"
category (to be defined during the talk) that only allows some compositions
of morphisms. The construction builds upon the theorem of Andy Chermak that
a saturated fusion system is always realized by a (suitably unique) partial
group -- and Chermak's concept of a partial group will be a special kind
partial category.

Every partial category can be seen to give rise to a actual category
enriched in simplicial sets via a very explicit procedure, and we shall see
that the proposed orbit category restricts to a classical category when
considering "sufficiently large" subgroups of S and that we recover the old
definition of an orbit category for F. This joint project with Rémi Molinier
is very much a work in progress, and as such the talk will contain many more
conjectures than theorems (with exception of the previous line).


Tarih: 3 Aralık 2018 Pazartesi, 10:40 - 11:50 

Bilkent Matematik Bölümü Seminer Odası SA - 141 

Konuşma öncesinde çay-kurabiye ikramı yapılacaktır. 
İlgilenen herkes davetlidir. 

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