GROW@Frankfurt 2025 is for all students of underrepresented gender identities in mathematics, especially female students, who are interested in learning about graduate programmes and further opportunities in research, both within and outside academia.

The Github repo is: kbuzzard/ClassFieldTheory.

I formalized part of Tate cohomology and local fields.

Class Field Theory in its cohomological form is one of the highlights of early 20th century mathematics, and is now understood as the abelian case of the Langlands Philosophy. Although it sounds like science fiction to many mathematicians, some computer scientists are arguing that AI methods are progressing so fast that soon computers will be helping humans to push back the boundaries of research in the Langlands Philosophy. However, there is currently no concrete evidence that this is happening. Furthermore, using a language model alone to do mathematics at this level is problematic, because language models are error-prone, and one error in a mathematical argument invalidates it.

This summer school does not have anything to do with AI, but it has a lot to do with class field theory. During the school, we will be teaching class field theory to the Lean theorem prover. You can imagine the school as a group of people collaborating on writing a Bourbaki-like document explaining class field theory. Or you can imagine it as a group of people turning class field theory into a bunch of levels of a puzzle game and then solving these levels. Or you can imagine it as a group of people creating training data for a theorem prover-backed AI which can then try and learn some of these interesting mathematical ideas.

I formalized lemmas regarding geometrically irreducibility of a ring, and its relation to tensor products. And shown this coincides with the same notion in scheme world.

This workshop is aimed primarily at PhD students with an interest in formalising results from algebraic geomery using the Lean proof assistant. Participants will work in teams on formalisation projects designed by our guest speakers.