Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

June 27, 2022

Compositional Modeling with Decorated Cospans

Posted by John Baez

It’s finally here: software that uses category theory to let you build models of dynamical systems! We’re going to train epidemiologists to use this to model the spread of disease. My first talk on this will be on Wednesday June 29th. You’re invited!

Compositional modeling with decorated cospans, Graph Transformation Theory and Practice (GReTA) seminar, 19:00 UTC, Wednesday 29 June 2022.

You can attend live on Zoom if you click here. You can also watch it live on YouTube, or later recorded, here.

Posted at 6:47 PM UTC | Permalink | Post a Comment

June 22, 2022

Motivating Motives

Posted by John Baez

I gave an introductory talk on Grothendieck’s ‘motives’ at the conference Grothendieck’s Approach to Mathematics at Chapman University in late May.

Now the videos of all talks at this conference are on YouTube — including talks by Kevin Buzzard, Colin McLarty, Elaine Landry, Jean-Pierre Marquis, Mike Shulman and other people you’ve heard about on this blog.

Posted at 5:32 PM UTC | Permalink | Followups (2)

June 20, 2022

Hoàng Xuân Sính

Posted by John Baez

During the Vietnam war, Grothendieck taught math to the Hanoi University mathematics department staff, out in the countryside. Hoàng Xuân Sính took notes and later did a PhD with him — by correspondence! She mailed him her hand-written thesis. She is the woman in this picture:

As you might guess, there’s a very interesting story behind this. I’ve looked into it, but what I found raises even more questions. Hoàng Xuân Sính’s life really deserves a good biography.

Posted at 8:08 PM UTC | Permalink | Followups (14)

June 18, 2022

Compositional Thermostatics (Part 4)

Posted by John Baez

guest post by Owen Lynch

This is the fourth and final part of a blog series on this paper:

• John Baez, Owen Lynch and Joe Moeller, Compositional thermostatics.

In Part 1, we went over our definition of thermostatic system: it’s a convex space XX of states and a concave function S:X[,]S \colon X \to [-\infty, \infty] saying the entropy of each state. We also gave examples of thermostatic systems.

In Part 2, we talked about what it means to compose thermostatic systems. It amounts to constrained maximization of the total entropy.

In Part 3 we laid down a categorical framework for composing systems when there are choices that have to be made for how the systems are composed. This framework has been around for a long time: operads and operad algebras.

In this post we will bring together all of these parts in a big synthesis to create an operad of all the ways of composing thermostatic systems, along with an operad algebra of thermostatic systems!

Posted at 11:28 PM UTC | Permalink | Followups (2)

June 15, 2022

Graded Modalities

Posted by David Corfield

I’m hosting a workshop tomorrow (13:00-17:00 UK time (UTC+1), Thursday 16 June 2022) which explores what common ground there may be in the treatment of graded modalities by linguistics, computer science and philosophy. It’s a hybrid event (in-person and online) and all are welcome, details here.

You very much ought to come along.

A fine example of a graded modality.

Posted at 12:49 PM UTC | Permalink | Followups (1)