Weekly update (8/9/2026)

I seem to be rolling out these later and later. So, I finally put it on my calendar. We’ll see if it will help me being more consistent!

No more funding. This week we heard that the last possibility for funding for this year got rejected, which means I have no funding for next year! Still trying to understand what happens to my position at the university. It is clear building a long-term research program like ours with that piece-meal unstable funding is not possible.

Switching away from UMich AI tools. So far, I timidly started using some AI tools to help with some proofs and review. I was using the one provided freely by the University, but it is essentially a web chat and it cannot review my files directory. We decided to use some of the donations to get a month of ChatGPT. It seems to be working a lot better, and 20$ a month is something we can afford for now. So, thanks to all that donated!

Basis for affine sets. Demitri, one of our students, have been working on recycling the proofs about basis and linear independence from vector space to ensemble spaces (which are proven to be affine sets: sets closed under affine combinations). It’s already integrated in the master branch, and he is looking into generalizing the cardinality arguments as well.

More work on Quantum Mechanics. I worked a lot more on putting together all the pieces we have for quantum for an article that is due in two weeks. Some of the issues will have to remain open, but there are interesting ideas that may work out long term. For example, one of the problem is that, once you abandon Hilbert spaces, you don’t have a spectral theorem so even defining density operators is a problem. However, nuclear spaces have other properties that can help. Without going too much into detail, it seem that assuming the existence of a Hamiltonian that allows Gibbs state for every value of beta can be used to show that the space has to be nuclear (in fact, Montel). This is yet another hint that quantum mechanics is effectively a theory of thermodynamic equilibria.

I hope to have a draft on the archive in the next two months.