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December 4, 2023
Magnitude 2023
Posted by Tom Leinster
I’m going to do something old school and live-blog a conference: Magnitude 2023, happening right now in Osaka. This is a successor to Magnitude 2019 in Edinburgh and covers all aspects of magnitude and magnitude homology, as well as hosting some talks on subjects that aren’t magnitude but feel intriguingly magnitude-adjacent.
Slides for the talks are being uploaded here.
What is magnitude? The magnitude of an enriched category is the canonical measure of its size. For instance, the magnitude of a set (as a discrete category) is its cardinality, and the magnitude of an ordinary category is the Euler characteristic of its nerve. For metric spaces, magnitude is something new, but there is a sense in which you can recover from it classical measures of size like volume, surface area and dimension.
What is magnitude homology? It’s the canonical homology theory for enriched categories. The magnitude homology of an ordinary category is the homology of its classifying space. For metric spaces, it’s something new, and has a lot to say about the existence, uniqueness and multiplicity of geodesics.
Let’s go!
December 1, 2023
Adjoint School 2024
Posted by John Baez
Are you interested in applying category-theoretic methods to problems outside of pure mathematics? Apply to the Adjoint School!
Apply here. And do it soon.
December 31, 2023. Application Due.
February - May, 2024. Learning Seminar.
June 10 - 14, 2024. In-person Research Week at the University of Oxford, UK.
Seminar on This Week’s Finds
Posted by John Baez
I wrote 300 issues of a column called This Week’s Finds, where I explained math and physics. In the fall of 2022 I gave ten talks based on these columns. I just finished giving eight more! Now I’m done.
Here you can find videos of these talks, and some lecture notes:
Topics include Young diagrams and the representation theory of classical groups, Dynkin diagrams and the classification of simple Lie groups, quaternions and octonions, the threefold way, the periodic table of -categories, the 3-strand braid group, combinatorial species, and categorifying the harmonic oscillator.
If my website dies, maybe these lectures will still survive on my YouTube playlist.