Here, I collect some mathematical texts I've written and which might be of someone's interest.
Notes for my talk at the Kleine AG in Bonn about modular curves, modular forms, and Hodge structures.
My Master's Thesis: Topological Algebra. In this thesis I synthesize two possible approaches to generalized schemes and the connections between them; most of the results are well-known (although not always written down) but some technical results are new (for example some of the bussiness with small sheaves). Then I give bunch of examples and show how they fit in this framework - e.g. F_1 schemes and adic spaces. Then I introduce condensed sets and outline one more example: analytic spaces of Scholze and Clausen (now outdated and replaced by analytic stacks).
Very old:
My Bachelor Thesis: A^1 Homotopy Theory. In this text, I try to promote the idea that (pre)sheaves are generalized spaces. Then I upgrade that to homotopical context. After that, and after explaining some algebraic geometry, I am able to introduce A^1 homotopy theory and outline some interesting applications.
My assignment for Algebra IV course: Sheaf cohomology - a short survey.pdf.
Slides for the talk I've given in Reading seminar from category theory: Enriched categories, weighted colimits.pdf. I've tried to explain how we can view weighted colimits as a special case of the functor tensor product and how we can present enriched Kan extensions using that fact.
Slides for yet another talk I've given in Reading seminar: Tangent structures, part 1, part 2, part 3. I talked about various examples of categories equipped with a notion of a tangent space.
Very unofficial text: Kähler differentials.pdf. I was learning those stuff for a better understanding of étale morphisms and I've managed to collect some fun facts.