Mathematical writings

Prerequisites to the Langlands Program

Synopsis. This mammoth project collects prerequisites in order to even try to understand the Langlands program. This is more of a hobby project of mine in learning and relearning much material, quite possibly not really related to the Langlands program, but interesting to me nonetheless. It tries to cover a broad array of topics, and number theory, homological algebra and modular forms are still missing. I'll work on it in my spare time.

Lecture notes

If I attend lectures, I always live tech them; some of them more complete than others. Here are the lecture notes I find worth presenting.

Essays

Why AI won't replace the job of mathematicians – a cultural argument

This is an idea for another essay. TBA.

Elegant physics problems (July 2026)

Synopsis. Some people like to solve problems without pencil and paper, keeping everything in their head. Naturally, the solutions will become less calculation-prone and much more geometric. Here, I present three physics problems, including their solutions, which have unexpected and beautiful solutions.

Turtles all the way down (June 2026)

To be published at the Mathematical Essays in Bonn initiative.

Synopsis. Although morally not important, many forget about size issues when studying category theory. I think that neglecting these technical problems could lead to wrong results if not careful. I'll cover two ways of resolution: by introducing classe (the standard) or by introducing Grothendieck universes (popular within algebraic geometry/topos theory). Their strengths will be demonstrated by means of three examples: the Yoneda lemma, properties of limits, and existence of Kan extensions. The last example shows that you can't run away from the truth, whichever formalism you use.