John C. Baez's Blog, page 52

Applied Category Theory 2019

I hope to see you at this conference!

• Applied Category Theory 2019, July 15-19, 2019, Oxford, UK.

Applied category theory is a topic of interest for a growing community of researchers, interested in studying systems of all sorts using category-theoretic tools. These systems are found in the natural sciences and social sciences, as well as in computer science, linguistics, and engineering. The background and experience of our members is as varied as the systems being studied. The goal of the...

Fermat Primes and Pascal’s Triangle

If you take the entries Pascal’s triangle mod 2 and draw black for 1 and white for 0, you get a pleasing pattern:

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The th row consists of all 1’s. If you look at the triangle consisting of the first rows, and take the limit as you get a fractal called the Sierpinski gasket. This can also be formed by repeatedly cutting triangular holes out of an equilateral triangle:

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Something nice happens if you interpret the rows of Pascal’s triangle mod 2 as numbers written in binary:

1 = 1
11 = 3
101...

From Classical to Quantum and Back

Damien Calaque has invited me to speak at FGSI 2019, a conference on the Foundations of Geometric Structures of Information. It will focus on scientific legacy of Cartan, Koszul and Souriau. Since Souriau helped invent geometric quantization, I decided to talk about this. That’s part of why I’ve been writing about it lately!

I’m looking forward to speaking to various people at this conference, including Mikhail Gromov, who has become interested in using category theory to understand biolog...

Systems as Wiring Diagram Algebras

 

Check out the video of Christina Vasilakopoulou’s talk, the third in the Applied Category Theory Seminar here at U. C. Riverside! It was nicely edited by Paola Fernandez and uploaded by Joe Moeller.

Abstract. We will start by describing the monoidal category of labeled boxes and wiring diagrams and its induced operad. Various kinds of systems such as discrete and continuous dynamical systems have been expressed as algebras for that operad, namely lax monoidal functors into the category of...

Symposium on Compositional Structures 3

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One of the most lively series of conferences on applied category theory is ‘SYCO’: the Symposium on Compositional Structures. And the next one is coming soon!

• Symposium on Compositional Structures 3, University of Oxford, 27-28 March, 2019.

The Symposium on Compositional Structures (SYCO) is an interdisciplinary series of meetings aiming to support the growing community of researchers interested in the phenomenon of compositionality, from both applied and abstract perspectives, and in par...

Classification Problems in Symplectic Linear Algebra

 

Last week Jonathan Lorand spoke at the Applied Category Theory Seminar here at UCR. Check out the video of his talk above, and also his talk slides.

Abstract. 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 po...

Geometric Quantization (Part 8)

 

Let’s start with a puzzle:

Puzzle. You measure the energy and frequency of some laser light trapped in a mirrored box and use quantum mechanics to compute the expected number of photons in the box. Then someone tells you that you used the wrong value of Planck’s constant in your calculation. Somehow you used a value that was twice the correct value! How should you correct your calculation of the expected number of photons?

I’ll give away the answer to the puzzle below, so avert your eyes...

Applied Category Theory Course – Videos

Yay! David Spivak and Brendan Fong are teaching a course on applied category theory based on their book, and the lectures are on YouTube! Here are the first two videos:

Their book is free here:

• Brendan Fong and David Spivak, Seven Sketches in Compositionality: An Invitation to Applied Category Theory.

If you’re in Boston you can actually go to the course. It’s at MIT January 14 – Feb 1, Monday-Friday, 14:00-15:00 in room 4-237.

They taught it last year too, and last year’s YouTube video...

The Mathematics of the 21st Century

Abstract. The global warming crisis is part of a bigger transformation in which humanity realizes that the Earth is a finite system and that our population, energy usage, and the like cannot continue to grow exponentially. If civilization survives this transformation, it will affect mathematics—and be affected by it—just as dramatically as the agricultural revolution or industrial revolution. We should get ready!

Check out the video of my talk, the first in the Applied Category Theory Semi...

Mathematics in the 21st Century

Abstract. The global warming crisis is part of a bigger transformation in which humanity realizes that the Earth is a finite system and that our population, energy usage, and the like cannot continue to grow exponentially. If civilization survives this transformation, it will affect mathematics—and be affected by it—just as dramatically as the agricultural revolution or industrial revolution. We should get ready!

Check out the video of my talk, the first in the Applied Category Theory Semi...