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SUMMARY:Mathematics colloquium
DTSTART:20190912
DTEND:20190912
DESCRIPTION: \;
"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.
LOCATION:Chemin du Cyclotron\, 2 CYCL01\, Bâtiment Marc de Hemptinne\, Louvain-la-Neuve 1348\, BE
DTSTAMP:20200603
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