Forthcoming Maths Seminar - 12 September 2006

[Mabilo Koutou]

M A T H E M A T I C S   S E M I N A R S   2006


Tuesday, 12 September, at 14.00 hrs.


Dr. Christian Valqui
(Instituto de Mathematicas y Ciencias Afines, Lima, Peru)


Closed model categories in noncommutative geometry


Abstract:

We begin with the construction of Serre fibrations in topological 
spaces. Together with weak equivalences and cofibrations they yield a 
so-called closed model category (CMC). A similar structure of 
fibrations, cofibrations and weak equivalences is found in simplicial 
spaces. Moreover, the two model categories are equivalent in a certain 
sense (Quillen equivalent), which is a result that motivated much of 
the theory of CMC's. We then analyse different CMC structures on 
complexes of modules, pro-modules and pro-algebras. Finally, we review 
recent results in KK-theory, namely the description of topological 
K-theory via CMC's and the description of the Baum-Connes Conjecture in 
terms of derived functors on triangulated categories.


VENUE:  SEMINAR ROOM
(Main Building, first floor)