Notes about commutative / homological algebra, sheaf theory and algebraic geometry. In the future this ought to be a comprehensive introduction to algebraic geometry. (Work in progress.)

The Hodge decomposition follows directly from a basic result on elliptic differential operators. This result is usually treated as a black-box in a lot of references. The goal of these notes is to demystify its proof.

Little notes explaining a surprisingly not-so-well-known corollary of the Yoneda lemma, which says that we can define an adjoint functor by only specifying how it acts on objects.

We use exponential sums as "an excuse" to learn lots of interesting ideas in number theory and algebraic geometry. These notes were strongly influenced by N. Katz course in Orsay and by J. Fresán Séminaire Bourbaki on the subject.

Quick notes about a very beautiful proof of the fact that a finite division ring is commutative using the Chevalley-Warning theorem (which is incredible by itself).

These notes contain a (very) brief introduction to complex analysis in one and several variables, and begin to explain some concepts of complex geometry. The first chapter is mostly done but the rest is quite rough. So caveat emptor.

Notes about the tannakian formalism, about D-modules and about the algebraic group generated by a holonomic D-module. This is a memoir about an internship with Javier Fresán.

Short notes about the étale fundamental group. This is a memoir about an internship with Antoine Ducros. (In french.)

Really brief notes about scheme theory, culminating into the Riemann-Roch theorem. This is a memoir about internships with Gaëtan Chenevier and Benjamin Schraen. (In french.)

An introduction to the Masur-Veech volumes of the moduli space of abelian differentials. This is a memoir about an internship with Carlos Matheus. (In french.)

Notes about the basic theory of Lie groups / algebra and their representation theory. This is a memoir about an internship with J. J. Ramón-Marí. (In my freshman year.)

Some notes I wrote about analysis in my freshman year. I won't finish this since basically every idea that I had for this project was beautifully implemented in the amazing book Spaces: An Introduction to Real Analysis by T. Lindstrøm.

These are the solutions of some of the exercises in P. Aluffi's book Algebra: Chapter 0. About half of the solutions were made by Ricardo Canesin and the other half split by Thiago Landim and myself.

These are the solutions of some of the exercises in W. Rudin's book Real and Complex Analysis. About half of the solutions were made by Thiago Landim and half were made by myself.

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