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December 15, 2024
Random Permutations (Part 14)
Posted by John Baez
I want to go back over something from Part 11, but in a more systematic and self-contained way.
Namely, I want to prove a wonderful known fact about random permutations, the Cycle Length Lemma, using a bit of category theory. The idea here is that the number of -cycles in a random permutation of things is a random variable. Then comes a surprise: in the limit as , this random variable approaches a Poisson distribution with mean . And even better, for different choices of these random variables become independent in the limit.
I’m stating these facts roughly now, to not get bogged down. But I’ll state them precisely, prove them, and categorify them. That is, I’ll state equations involving random variables — but I’ll prove that these equations come from equivalences of groupoids!
December 10, 2024
Martianus Capella
Posted by John Baez
I’ve been blogging a bit about medieval math, physics and astronomy over on Azimuth. I’ve been writing about medieval attempts to improve Aristotle’s theory that velocity is proportional to force, understand objects moving at constant acceleration, and predict the conjunctions of Jupiter and Saturn. A lot of interesting stuff was happening back then!
As a digression from our usual fare on the -Café, here’s one of my favorites, about an early theory of the Solar System, neither geocentric nor heliocentric, that became popular thanks to a quirk of history around the time of Charlemagne. The more I researched this, the more I wanted to know.
December 4, 2024
ACT 2025
Posted by John Baez
The Eighth International Conference on Applied Category Theory (https://easychair.org/cfp/ACT2025) will take place at the University of Florida on June 2-6, 2025. The conference will be preceded by the Adjoint School on May 26-30, 2025.
This conference follows previous events at Oxford (2024, 2019), University of Maryland (2023), Strathclyde (2022), Cambridge (2021), MIT (2020), and Leiden (2019).
Applied category theory is important to a growing community of researchers who study computer science, logic, engineering, physics, biology, chemistry, social science, systems, linguistics and other subjects using category-theoretic tools. The background and experience of our members is as varied as the systems being studied. The goal of the Applied Category Theory conference series is to bring researchers together, strengthen the applied category theory community, disseminate the latest results, and facilitate further development of the field.
If you want to give a talk, read on!