27 April 2018:
Here is some of this week's progress. A lot has been happening at the Applied Category Theory School, but I'll start with other things:
1) Blake Pollard got a 3-year National Research Council grant to continue his work at NIST and Carnegie Mellon! This is really great!
2) Daniel Cicala applied for and received a Dissertation Year Fellowship, which will support him for one quarter next year!
3) Joe Moeller put a paper on the arXiv:
. Network models, which abstractly are given by lax symmetric monoidal functors, are used to construct operads for modeling and designing complex networks. Many common types of networks can be modeled with simple graphs with edges weighted by a monoid. A feature of the ordinary construction of network models is that it imposes commutativity relations between edge components. Because of this, it cannot be used to model networks with bounded degree. In this paper, we construct a network model which can model networks with bounded degree. To do this, we generalize Green's graph products of groups to pointed categories which are finitely complete and cocomplete.
4) The Adjoint School part of Applied Category Theory 2018 is done! Four mentors - Aleks Kissinger, Pawel Sobocinski, Martha Lewis and myself - worked with teams of students to solve problems on causality, linear dynamical systems, linguistics and biology, respectively.
My team, from left to right here, consisted of Blake, Maru Saruzola doing algebraic K-theory at Cornell, Fabrizio Genovese working in Bob Coecke's quantum group in computer science at Oxford, and Jonathan Lorand doing symplectic geometry in a postdoc in Zurich:
We discovered some surprising results about the math of ATP coupling, and now we need to write them up. Meanwhile, Daniel and Joe were working with Pawel Sobocinski on circuits and signal flow diagrams, rediscovering some results that Brandon Coya and I have already written up, but maybe also some generalizations involving cartesian bicategories. Jade Master worked with Martha Lewis on translation using Lambek's pregroup grammars. Lots of great stuff!