[Turkmath:9034] Bilkent'te temsil teorisi seminerleri

[Ergun Yalcin]

Degerli liste uyeleri,

Onumuzdeki hafta Bilkent Universitesi Matematik bolumunde
temsil teorisi uzerine uc seminer olacaktir. Seminerlerin baslik
ve kisa ozetlerini asagida bulabilirsiniz. Ilgilenen butun
matematikcileri bekliyoruz. 

Bu aktivite Tubitak Konuk Bilim Adami programi tarafindan 
kismi olarak desteklenmektedir.

Saygilarimla,
Ergun Yalcin


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1) Speaker: Serge Bouc (Universite de Picardie)

Date: May 28, Tuesday, 14:00-15:00 

Title : The algebra of essential relations on a finite set

Abstract : In this joint work with Jacques Thévenaz, we study the 
structure of the algebra E(X) of essential relations on a finite 
set X: this algebra (which doesn't seem to have been considered 
so far) is the quotient of the algebra of the monoid of all 
relations on X by the submodule generated by relations which 
factor through a (strictly) smaller set. In particular, we determine 
all the simple E(X)-modules. 


2) Speaker: Radu Stancu (Universite de Picardie)

Date: May 29, Wednesday, 14:00-15:00

Title: Saturated fusion systems and idempotents in the double Burniside ring

Saturated fusion systems were introduced by Puig as a generalization of the $p$-local structure of a finite group or of a block algebra of a finite group. Broto, Levi and Oliver introduced the notion of characteristic biset associated to a saturated fusion system. This biset is not unique but Ragnarsson proved that there is a unique characteristic idempotent in the p-completed double Burnside ring associated to a saturated fusion system.

In this talk, based o a joint work with Kari Ragnarsson, I will give a characterization of saturated fusion systems on a $p$-group $S$ in terms of idempotents in the $p$-local double Burnside ring of $S$ that satisfy a Frobenius reciprocity relation. This helps us to reformulate fusion-theoretic phenomena in the language of idempotents and give some applications in stable homotopy.



3) Speaker: Peter Webb (University of Minnesota)

Date: May 30, Thursday, 14:00-15:00

Title: Doing group theory with categories

Abstract: Many of the constructions which we do in group theory can be done in a more general context: that of categories. There is a cohomology theory of categories with interpretations of low-dimensional cohomology analogous to what happens for groups. There is a Gruenberg resolution, a Burnside ring, we can define Mackey functors on categories, there are extensions of categories: the list goes on. Historically many of these structures have been used to understand groups better, and this remains a motivation for studying the more recent generalizations. I will give an overview of some of the range of things that can done.

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