John Baez's Stuff

What's On This Site This Week's Finds - Latest Edition Fun Stuff Physics FAQ Nasty Stuff Seminar Serious Stuff Talks Diary n-Category Café nLab EUREKA

John Baez's Stuff

I'm a mathematical physicist. I specialize in n-categories and their applications, but I'm interested in many other things too. I like talking about them here.

What's New?

In "week293" of This Week's Finds, catch up on recent papers and books about n-categories. Hear about last weekend's Conference on the Mathematics of Environmental Sustainability and Green Technology at Harvey Mudd College. Read about Kenneth Golden's work on the fractal structure of brine in ice:

And learn how to think of networks of resistors as chain complexes which are also morphisms in a category.

Are squares A and B the same color?

Yes! If you don't believe me, look at this, and then read the Wikipedia article about this illusion invented by Edward Adelson of MIT.

For a related illusion, try this.

My students and I got a grant from the Foundational Questions Institute to work on categorifying fundamental physics. We've been hard at work:

Alex Hoffnung, Christopher Walker and I wrote a paper that unifies linear algebra and the study of groupoids: Higher-Dimensional Algebra VII: Groupoidification. This will appear in Theory and Application of Categories. We are now working on the next two papers in this series, which will treat Hecke algebras and Hall algebras in more detail.
Alex Hoffnung, Chris Rogers and I wrote a paper on Lie 2-algebras in classical field theory: Categorified Symplectic Geometry and the Classical String, which will appear in Communcations in Mathematical Physics. Chris and I then wrote a followup: Categorified Symplectic Geometry and the String Lie 2-Algebra, which will appear in Homology, Homotopy and Applications.
Alex Hoffnung and I wrote a paper on the foundations of differential geometry: Convenient Categories of Smooth Spaces, which will appear in in Transactions of the American Mathematical Society.
John Huerta and I wrote a paper on the beautiful patterns of particle physics: The Algebra of Grand Unified Theories, which will appear in Bulletin of the American Mathematical Society. Then we wrote one called Division Algebras and Supersymmetry I, which will appear in Proceedings of the NSF/CBMS Conference on Topology, C*-Algebras, and String Theory. We're now working on the next in this series.

Mike Stay and I wrote a review of category theory and its applications: Physics, Topology, Logic and Computation: A Rosetta Stone, to appear in Bob Coecke's volume New Structures of Physics.

Also:

Aaron Lauda and I wrote a big expository paper called A Prehistory of n-Categorical Physics, which should appear in Deep Beauty: Mathematical Innovation and the Search for an Underlying Intelligibility of the Quantum World, edited by Hans Halvorson.
My former student Derek Wise, my colleague Laurent Freidel, his student Aristide Baratin and I wrote a paper on Infinite-Dimensional Representations of 2-Groups.

What's on This Site

This Week's Finds in Mathematical Physics (my column)
Fun Stuff (expository writings and other diversions)
Nasty Stuff (human rights, economics and other scandals)
Seminar (tons of course notes)
Serious Stuff (my actual research)
Talks (transparencies of my talks, info on forthcoming talks)
Diary (random thoughts)

Also try my blog at:

The n-Category Café

For common questions about physics, you can't beat this:

Frequently Asked Questions in Physics

I don't maintain this Physics FAQ - Don Koks does, so please send any comments about it to him, not me!

If reading my stuff makes you want to ask questions, take a look at this.

Click here to see how many hits this page gets.

The universe is full of magical things, patiently waiting for our wits to grow sharper. - Eden Philpotts