Non-commutative Stone duality: from analysis to algebra
Mark Lawson (Heriot-Watt University)
Thursday 8th February 16:00-17:00 Maths 311B
The goal of this talk is to explain the duality between a class of inverse monoids, called Boolean inverse monoids, and a class of \'etale groupoids, called Boolean groupoids. This duality extends the classical duality discovered by Stone in 1937 between Boolean algebras and Boolean spaces from a commutative to a non-commutative setting. Although algebraic, both theories have their roots in functional analysis. I shall explain what these are and raise some questions about how this theory might be developed.