Speaker: Philip Scott
Time & Place: Friday Sept. 12, 11.30-1 , KED B015
Title: An Introduction to MV and Effect Algebras I.
Abstract: We introduce MV Algebras (the algebras of certain many-valued logics).
These were developed by C.C. Chang in the mid-1950's. They describe the
algebras of probabilistic/fuzzy logics with truth values in [0,1],
developed by the Polish school of logicians in the 1920's: Lukasiewicz,
Lesniewski, Tarski, et. al. Surprisingly, Mundici, in the 1980's showed,
a deep connection of such algebras with Elliott's program of
classification of AF C*-algebras, as well as work on dimension groups.
In recent work with Mark Lawson, we have given a coordinatization (in
the sense of von Neumann) of all denumerable MV-algebras, using a
mixture of dimension group theory and a new theory of AF inverse monoids
(e.g. associated with Bratteli diagrams).
Our work transitions through another (independent) theory, Effect
Algebras, which arose in the 1990's in quantum measurement theory by
certain mathematical physicists (Foulis, Bennet, Pulmannova). These are
partial algebras, related to sharp and unsharp measurement theory.
We shall begin a leisurely introduction to this work.
[Joint work with Mark Lawson]
------------------------------------------------------------- Speaker:
Jonathan Scott (Cleveland State University)
Time& Place: Friday Oct. 31, 11.30am, KEDB015
Title: Metrics arising from Persistent Homology
Abstract: The interleaving distance gives a metric on barcodes arising
from persistent homology calculations. We look at this metric from a
category-theoretical standpoint. As a result, we see that the
interleaving distance can be defined in a wide variety of functor
categories.
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Speaker: Simon Fortier-Garceau (Ottawa)
Time & Place: Friday Nov. 7, 11.30am, KEDB015
Title : Spatially induced concurrency for presheaves of
labelled transition systems
Abstract : We study how to model concurrent processes in spatially
separated regions via presheaf and sheaf models. The presheaves in
question describe the spatial distribution of processes; hence the terms
``spatially induced concurrency'' (SI-concurrency).
We start by discussing labelled transition systems (LTS) and how
concurrency can be represented in such systems by the addition of an
independence relation on labels yielding an asynchronous labelled
transition system (ALTS). Then, we look into an example of an LTS-valued
presheaf taken from G. Malcolm and J. Goguen's work, and explore how the
notion of SI-concurrency is realized there. Finally, we present a class
of LTS-valued presheaves that have SI-concurrency and we seek the
minimal conditions by which this property can be generalized to the
entire class of LTS-valued presheaves.
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Speaker: Sakif Hossain Khan (Ottawa)
Time & Place: Friday Nov. 21, 11.30am, LMX 242
(Please note: not the usual venue!!)
Title: Higher Order Isotropy
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Speaker: Robert Furber (Radboud University Nijmegen)
Time & Place: Friday Jan. 16, 2.30pm , KEDB004
Title: Effect Algebras and Convex Sets
Abstract:
Effect algebras are a generalization of Boolean algebras, coming from
quantum logic. In this talk I will explain what they are and the
motivation from quantum physics and probability. This leads to changing
the notion of a truth assignment, to take values in the unit interval
[0,1]. The set of all of these for a given effect algebra is a convex
set called the state space. If time permits, I will explain a duality
for effect algebras analogous to Stone duality for Boolean algebras,
based on a theorem of Kadison.
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Speaker: Marc Bagnol (Ottawa)
Time & Place: Friday Jan. 23rd, 2.30pm, KED B004
Title: The resolution semiring and implicit complexity
Abstract:
The resolution semiring R is an algebraic structure with a product based
on the resolution rule of logic programming. It was originally
introduced to build dynamic models of linear logic and lambda-calculus,
in the setting of the geometry of interaction (GoI) research program:
one can build from it a traced monoidal category with a "GoI situation".
As such, it can serve as a tool to study complexity theory in a
machine-independant (ie. implicit) way: we will see that the complexity
classes LOGSPACE and PTIME can indeed be captured by specific
sub-semirings of R.
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Speaker: Frank Roumen
Time & Place: Jan. 30, 2.30pm, KED B004
Title: Effect algebroids
Abstract: Effect algebras are a generalization of Boolean algebras,
useful for studying quantum logic. There are many similarities between
effect algebras and abstract circles, which are structures occuring in
topos theory and cyclic cohomology. We will define a common
generalization of these two structures, called an effect algebroid. This
allows us to combine many features of the two theories, for example, it
provides a notion of cohomology of effect algebras.