We’re going to have a seminar on applied category theory here at U. C. Riverside! My students have been thinking hard about category theory for a few years, but they’ve decided it’s time to get deeper into applications. Christian Williams, in particular, seems to have caught my zeal for trying to develop new math to help save the planet.

We’ll try to videotape the talks to make it easier for you to follow along. I’ll also start discussions here and/or on the Azimuth Forum. It’ll work best if you read the papers we’re talking about and then join these discussions. Ask questions, and answer any questions you can!

Here’s how the schedule of talks is shaping up so far. I’ll add more information as it becomes available, either here or on a webpage devoted to the task.

#### January 8, 2019: John Baez – Mathematics in the 21st century

I’ll give an updated synthesized version of these earlier talks of mine, so check out these slides and the links:

• The mathematics of planet Earth.

#### January 15, 2019: Jonathan Lorand – Problems in symplectic linear algebra

Lorand is visiting U. C. Riverside to work with me on applications of symplectic geometry to chemistry. Here is the abstract of his talk:

In this talk we will look at various examples of classification problems in symplectic linear algebra: conjugacy classes in the symplectic group and its Lie algebra, linear lagrangian relations up to conjugation, tuples of (co)isotropic subspaces. I will explain how many such problems can be encoded using the theory of symplectic poset representations, and will discuss some general results of this theory. Finally, I will recast this discussion from a broader category-theoretic perspective.

#### January 22, 2019: Christina Vasilakopoulou – Wiring diagrams

Vasilakopoulou, a visiting professor here, previously worked with David Spivak. So, we really want to figure out how two frameworks for dealing with networks relate: Brendan Fong’s ‘decorated cospans’, and Spivak’s ‘monoidal category of wiring diagrams’. Since Fong is now working with Spivak they’ve probably figured it out already! But anyway, Vasilakopoulou will give a talk on systems as algebras for the wiring diagram monoidal category. It will be based on this paper:

• Patrick Schultz, David I. Spivak and Christina Vasilakopoulou, Dynamical systems and sheaves.

but she will focus more on the algebraic description (and conditions for deterministic/total systems) rather than the sheaf theoretic aspect of the input types. This work builds on earlier papers such as these:

• David I. Spivak, The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits.

• Dmitry Vagner, David I. Spivak and Eugene Lerman, Algebras of open dynamical systems on the operad of wiring diagrams.

#### January 29, 2019: Daniel Cicala – Dynamical systems on networks

Cicala will discuss a topic from this paper:

• Mason A. Porter and James P. Gleeson, Dynamical systems on networks: a tutorial.

His leading choice is a model for social contagion (e.g. opinions) which is discussed in more detail here:

• Duncan J. Watts, A simple model of global cascades on random networks.