John C. Baez's Blog, page 42

Open Markov Processes

I’m giving a talk on some work I did with Kenny Courser. It’s part of the ACT2020 conference, and it’s happening on 20:40 UTC on Tuesday July 7th, 2020. (That’s 1:40 pm here in California, just so I don’t forget.)

Like all talks at this conference, you can watch it live on Zoom or on YouTube. It’ll also be recorded, so you can watch it later on YouTube too, somewhere here.

You can see my slides now, and read some other helpful things:

• Coarse-graining open Markov processes.

Abstract. We ...

Getting to the Bottom of Noether’s Theorem

Most of us have been staying holed up at home lately. I spent the last month holed up writing a paper that expands on my talk at a conference honoring the centennial of Noether’s 1918 paper on symmetries and conservation laws. This made my confinement a lot more bearable. It was good getting back to this sort of mathematical physics after a long time spent on applied category theory. It turns out I really missed it.

While everyone at the conference kept emphasizing that Noether’s 1918 paper ...

ACT2020 Program

Applied Category Theory 2020 is coming up soon! After the Tutorial Day on Sunday July 6th, there will be talks from Monday July 7th to Friday July 10th. Here is the program—click on it to download a more readable version:

All talks will be live on Zoom. Recorded versions should appear on YouTube later.

Here are the talks! They come in three kinds: keynotes, regular presentations and short industry presentations. Within each I’ve listed them in alphabetical order by speaker: I believe th...

ACT2020 Tutorial Day

If you’re wanting to learn some applied category theory, register for the tutorials that are taking place on July 5, 2020 as part of ACT2020!

Applied category theory offers a rigorous mathematical language and toolset for relating different concepts from across math, science, and technology. For example, category theory finds common patterns between geometry (shapes), algebra (equations), numbers, logic, probability, etc. Applied category theory (ACT) looks for how those very same patterns exte...

Thermalization

I’m wondering if people talk about this. Maybe you know?

Given a self-adjoint operator that’s bounded below and a density matrix on some Hilbert space, we can define for any a new density matrix

I would like to call this the thermalization of when is a Hamiltonian and where is the temperature and is Boltzmann’s constant.

For example, in the finite-dimensional case we can take to be the identity matrix, normalized to have trace 1. Then is the Gibbs state at temperature : that is, th...

Categorical Statistics Group

As a spinoff of the workshop Categorical Probability and Statistics, Oliver Shetler has organized a reading group on category theory applied to statistics. The first meeting is Saturday June 27th at 17:00 UTC.

You can sign up for the group here, and also read more about it there. We’re discussing the group on the Category Theory Community Server, so if you want to join the reading group should probably also join that.

Here is a reading list. I’m sure the group won’t cover all these papers—we’...

Statistics for Category Theorists

As a spinoff of the workshop Categorical Probability and Statistics,

some people are now batting around the idea of having a reading group on statistics for category theorists. Here is a reading list compiled by Oliver Shetler:

• McCullagh, What is a statistical model?

• Morse and Sacksteder, Statistical isomorphism.

• Simpson, Probability sheaves and the Giry monad.

• Fritz, A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics.

• Jacobs, Probab...

ACT@UCR Seminar (Part 2)

The spring 2020 seminar on applied category theory at U.C. Riverside is done! Here you can see videos of all the talks, along with talk slides, discussions and more:

• John Baez: Structured cospans and double categories.

• Prakash Panangaden: A categorical view of conditional expectation.

• Jules Hedges: Open games: the long road to practical applications.

• Michael Shulman: Star-autonomous envelopes.

• Gershom Bazerman: A localic approach to the semantics of dependency, conflict, and concurren...

Values and Inclusivity in the ACT Community

In the tenth and final talk of this spring’s ACT@UCR seminar, Nina Otter led a discussion about diversity in the applied category theory community, with these speakers:

• Nina Otter: introduction, and some potential initiatives

• Jade Master: Experience in setting up an online research community for minorities in ACT

• Brendan Fong: Statement of values for ACT community

• Emily Riehl: Experience at MATRIX institute

• Christian Williams: Quick overview of ACT server

This is a change from her orig...

A Unified Framework for Equivalences in Social Networks

In the tenth and final talk of this spring’s ACT@UCR seminar, Nina Otter will tell us about the mathematics of social networks.

She will give her talk on Wednesday May 27th at 5 pm UTC, which is 10 am in California, or 1 pm on the east coast of the United States, or 6 pm in the UK. It will be held online via Zoom, here:

https://ucr.zoom.us/j/607160601

Afterwards we will talk at the Category Theory Community Server, here:

https://categorytheory.zulipchat.com/#narrow/stream/229966-ACT.40UCR-semina...