Math Colloquium, Manuel Reyes (Bowdoin): 'The spectrum problem for noncommutative rings and algebras'

Friday, November 7, 2014
4:15 PM - 5:05 PM (ET)
ESC 638
Event Type
Academic Calendar
Cameron Hill
Math/CS Colloquium

Abstract: The spectrum of a commutative algebra is a topological space, assigned in such a way that homomorphisms between algebras correspond to continuous functions between spaces. Since the spectrum provides geometric intuition to the study of commutative algebra, it seems natural to follow the tradition of noncommutative geometry and ask: what might be a useful spectrum for noncommutative algebras? I will discuss negative answers in the forms of obstructions, with surprising connections to the foundations of quantum physics. Then I will discuss some progress (joint work with Chris Heunen) toward a positive result, which provides a correspondence between certain operator algebras and 'noncommutative Boolean algebras' called active lattices.

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