Date(s) - 16/11/2016
3:15 pm - 4:30 pm
SICSA DVF Professor Philip J Scott from the University of Ottawa will be giving a talk titled “A Coorinatization of Countable MV algebras” at Heriot-Watt University.
Abstract: The algebras of many-valued Lukasiewicz logics (MV algebras) as well as the algebras of quantum measurement (Effect algebras) have undergone major development since the 1980s and 1990s; they have connections with a wide range of areas, from logic to operator algebras to mathematical physics.
I will give a brief introduction to MV algebras, as well as the moregeneral world of effect algebras. Time permitting, I hope to illustrate these notions by sketching recent results (with Mark Lawson) on coordinatization of countable MV-algebras using inverse semigroup theory. The structures involved, Boolean inverse monoids, have recently arisen in areas related to non-commutative Stone duality, aperiodic tilings, etc. We prove that every countable MV algebra is isomorphic to the lattice of principal ideals of certain Boolean inverse monoids. The specific class involved in the proof, AF inverse monoids, corresponds to AF C*-algebras and arises from Bratteli diagrams of countable dimension groups. If there’s time, further new directions by
F. Wehrung, D. Mundici, et. al. will be discussed.
P. J. Scott is a mathematical logician working in category theory, proof theory, and theoretical computer science. In 1986 he published the book Introduction to Higher Order Categorical Logic (Cambridge University Press) with J. Lambek, which has been highly inuential both in the development of categorical logic, and in its applications in theoretical computer science. In particular, the book establishes the close connections between various type theories, categories, and logics. It thus motivated later works on using category theory and related machinery in programming languages, as well as operational and denotational semantics.
Professor Scott is currently Associate Editor of the Cambridge journal Mathematical Structures in Computer Science, and a Coordinating Editor of the North-Holland journal Annals of Pure and Applied Logic. In Canada, his research funding comes from NSERC (Natural Sciences and Engineering Research Council of Canada). Since the early 1990s, Prof. Scott has published foundational papers in areas relating categorical logic to theoretical computer science.