27 June 2017:
More abstracts for our AMS special session on Applied Category Theory on November 4-5.
1) Kenny Courser:
* A bicategory of coarse-grained Markov processes.
> **Abstract.** If C is a category with finite colimits, D is a symmetric monoidal category and F is a lax symmetric monoidal functor from C to D, Fong has developed a theory of F-decorated cospans which are suitable for representing open dynamical systems. Indeed, Fong has shown the existence of a symmetric monoidal category consisting of objects of C and isomorphism classes of F-decorated cospans in C as morphisms. One application of this result is given by Baez, Fong and Pollard in which they construct a symmetric monoidal category whose morphisms are given by isomorphism classes of open Markov processes. Using a result of Shulman, we present a symmetric monoidal bicategory consisting of finite sets as objects,open Markov processes as morphisms and coarse-grainings of open Markov processes as 2-morphisms. (Received June 25, 2017)
2) Adam Yassine:
* Open systems in classical mechanics
> **Abstract.** Using the framework of category theory, we formalize the heuristic principles that physicists employ in constructing the Hamiltonians for open classical systems as sums of Hamiltonians of subsystems. First we construct a category where the objects are symplectic manifolds and the morphisms are spans whose legs are surjective Poisson maps. Using a slight variant of Fong’s theory of ”decorated” cospans, we then decorate the apices of our spans with Hamiltonians. This gives a category where morphisms are open classical systems, and composition allows us to build these systems from smaller pieces. (Received June 26, 2017)
Keep 'em coming! I'm still hoping that Brandon, Joseph and Christina will submit abstracts. John Foley may submit one too: it would be great to have him give a talk about how our Metron project is using operads for "compositional tasking". This would be a nice sequel to a talk by Joseph on the underlying math - namely, "network models" and the operads they give rise to.