Today I heard from David Benson that Jack Morava died yesterday. This comes as such a huge shock that I can’t help but hope Benson was somehow misinformed. Morava has been posting comments to the ...

Quick question. Classically the harmonic oscillator Hamiltonian is often written 1 2 ( p 2 + q 2), while quantum mechanically it gets some extra ‘ground state energy’ making the Hamiltonian ...

August 2025's Entries (BT) Diversity from (LC) Diversity Jack Morava Random Past Entries TeXnical Issues Sage advice on viewing this blog and posting comments thereon. Journal Publishers Hire the “Pit ...

Announcing the Clowder Project: a wiki and reference work for category theory built using the same general infrastructure and tag system of the Stacks Project.

Note: These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older ...

In Part 1, I explained my hopes that classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant k k approaches zero. In Part 2, I explained exactly what I mean ...

For questions 1 and 2, isn’t that true for any group G, not just the fundamental groups of a manifold? And moreover, I think of this as the definition of the profinite completion of a group: as an ...

Despite the “2” in the title, you can follow this post without having read part 1. The whole point is to sneak up on the metricky, analysisy stuff about potential functions from a categorical angle, ...

We discuss in this post how these questions led us to possible relations to information geometry. We would love to hear from you: Is magnitude an interesting invariant for information geometry? Is ...

Bijection statement Here is the statement as I understand it to be, framed as a bijection of sets. My chief reference is the wonderful book Elliptic Curves, Modular Forms and their L-Functions by ...

Last time I reviewed a bit of Bott periodicity. Now I want to start leading up to a question about it. It will take a while. So, this time, I will explain a wonderful one-to-one correspondence between ...