John C. Baez's Blog, page 24

The Algebra of Grand Unified Theories

In this long conversation, Timothy Nguyen and I talk about the fascinating mathematical patterns in the Standard Model that led people to grand unified theories:

For more details go here:

• John Baez and John Huerta, The algebra of grand unified theories, Bulletin of the American Mathematical Society 47 (2010), 483–552.

Seminar on This Week’s Finds

Here’s something new: I’ll be living in Edinburgh until January! I’m working with Tom Leinster at the University of Edinburgh, supported by a Leverhulme Fellowship.

One fun thing I’ll be doing is running seminars on some topics from my column This Week’s Finds. They’ll take place on Thursdays at 3:00 pm in Room 6206 of James Clerk Maxwell Building, home of the Department of Mathematics. The first will be on September 22nd, and the last on December 1st. They may be recorded.

The theme for th...

Joint Mathematics Meetings 2023

This is the biggest annual meeting of mathematicians:

• Joint Mathematical Meetings 2023, Wednesday January 4 – Saturday January 7, 2023, John B. Hynes Veterans Memorial Convention Center, Boston Marriott Hotel, and Boston Sheraton Hotel, Boston, Massachusetts.

As part of this huge meeting, the American Mathematical Society is having a special session on Applied Category Theory on Thursday January 5th.

I hear there will be talks by Eugenia Cheng and Olivia Caramello!

(Me too.)

You can submit an ...

Symposium on Compositional Structures 9

The Symposium on Compositional Structures is a nice informal conference series that happens more than once a year. You can now submit talks for this one.

• Ninth Symposium on Compositional Structures (SYCO 9), Como, Italy, 8-9 September 2022. Deadline to submit a talk: Monday 1 August 2022.

Apparently you can attend online but to give a talk you have to go there. Here are some details:

The Symposium on Compositional Structures (SYCO) is an interdisciplinary series of meetings aiming to sup...

Compositional Modeling with Decorated Cospans

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 record...

Hoàng Xuân Sính

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.

Hoàng Xuân Sính was born...

Tutorial on Categorical Semantics of Entropy

Here are two talks on the categorical semantics of entropy, given on Wednesday May 11th 2022 at CUNY. First one there’s one by me and then starting around 1:31:00 there’s one by Tai-Danae Bradley:

My talk is called “Shannon entropy from category theory”:

Shannon entropy is a powerful concept. But what properties single out Shannon entropy as special? Instead of focusing on the entropy of a probability measure on a finite set, it can help to focus on the “information loss”, or change in ent...

Shannon Entropy from Category Theory

I’m giving a talk at the Tutorial on Categorical Semantics of Entropy on May 11th. You can watch it live on Zoom or recorded later. Here’s the idea:

Shannon entropy is a powerful concept. But what properties single out Shannon entropy as special? Instead of focusing on the entropy of a probability measure on a finite set, it can help to focus on the “information loss”, or change in entropy, associated with a measure-preserving function. Shannon entropy then gives the only concept of inf...

Categorical Semantics of Entropy

There will be a workshop on the categorical semantics of entropy at the CUNY Grad Center in Manhattan on Friday May 13th, organized by John Terilla. I was kindly invited to give an online tutorial beforehand on May 11, which I will give remotely to save carbon. Tai-Danae Bradley will also be giving a tutorial that day in person:

• Tutorial: Categorical Semantics of Entropy, Wednesday 11 May 2022, 13:00–16:30 Eastern Time, Room 5209 at the CUNY Graduate Center and via Zoom. Organized by John...

Compositional Thermostatics (Part 4)

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 of states and a concave function 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 ...