"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.