1 June 2018:
This week's progress:
1) Adam Yassine is giving a talk on his work. And I may have forgotten to mention his May 14th talk in our network theory seminar!
- A category theoretic framework for analytical mechanics
Abstract. We initiate a program to formalize in a category theoretic framework the heuristic principles that physicists employ in constructing analytical mechanical models of classical physical systems. We work in the category of symplectic manifolds where morphisms are surjective Poisson maps. Decorated spans can be constructed in this category and the composition of isomorphism classes of decorated spans is defined using pullbacks. Certain Hamiltonian systems are mathematically described as compositions of isomorphism classes of decorated spans. The compositional elements correspond physically to the subsystems of the described system. A similar framework permits a category theoretic description of certain Lagrangian systems. A symmetric monoidal functor between the two categories translates between the Lagrangian and Hamiltonian perspectives.
2) My paper with Brandon, Props in network theory
, was accepted for publication in Theory and Applications of Categories
. This is the one where the referee thought we explained the symplectic geometry in too much detail, didn't understand the category theory, and passed it on to another referee. The second referee understood the category theory and liked the paper more!
We made the required changes, put the paper in TAC's format, and submitted it today. Now I can go back to fixing my paper with Brendan... which is another long story.
3) I got an email from Mario Rasetti, who heads ">ISI
, that research center in Torino. He wrote:
I presented your proposal to our Science Board and they: i) confirmed their eager intention to proceed with the idea to create strong mathematics group, mostly focused on algebraic topology and category theory, in support of our research on topological data analysys; ii) checked with the Board of Directors of the Foundation that fresh sustainable funds for such operation are not available right now, but will be made available - if an interesting project is presented - for 2019: iii) agreed that you would be an excellent leader for this operation, provided you would agree to spend an adequate fraction of your time in Torino. At this point you and I should try and meet in person (perhaps in New York, at the site that ISI has there) to discuss how realistic all this is for you.