Colloquium de mathématique

Louvain-La-Neuve

Le colloquium de mathématiques est une activité scientifique mensuelle de l'IRMP. Il consiste en un exposé d'une heure au cours duquel l'orateur présente un thème lié à la recherche en mathématiques. Le public cible est généraliste, il inclut l'ensemble des membres de l'IRMP: doctorants, post-docs et professeurs de tous les domaines de recherche. Les étudiants de master sont également les bienvenus.

Responsable du Colloquium : Prof. Pierre-Emmanuel Caprace

 

A venir...

Le jeudi 12 sept. 2019 à 16:30 → 17:30 au local CYCL 01 (M. de Hemptinne)

Alberto Facchini (U. di Padova) fera un exposé intitulé:

"Rings and their spectrum"

 

Abstract

Noncommutative geometry is a geometric approach to noncommutative algebra. The main motivation of noncommutative geometry is to extend various functors between spaces and functions to the noncommutative setting.  Spaces, which are geometric in nature, can be related to numerical functions on them, which in general form a commutative ring. Thus we have functors F:{spaces}->{commutative rings} and G:{commutative rings}->{spaces}, for instance the contravariant functor Spec:{commutative rings}->{(spectral) topological spaces}. It is tempting to hope that one could extend the spectrum to the noncommutative setting in order to construct the “underlying set of a noncommutative space.” We will try to discuss these things in a language understandable to everybody (i.e., to any mathematician...)

References

(1) M. Reyes, Obstructing extensions of the functor Spec to noncommutative rings, Israel J. Math. 192 (2012), 667-698.
(2) A. Facchini and L. Heidari Zadeh, On a partially ordered set associated to ring morphisms, J. Algebra 535 (2019), 456-479.
(3) A. A. Bosi and A. Facchini, A natural fibration for rings, submitted for publication, 2019.

Coffee, tea and snacks will be served from 3:45 pm in the hall near the CYCL01.