General writings

Recent-ish notes
Notes of Everything

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

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. 

Adjoints can be defined on objects

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.

Exponential Sums: a tour through number theory

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.

Wedderburn's Little Theorem

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).

Complex Geometry

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.

Tannakian Formalism for D-modules

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.

Le groupe Fondamental Étale

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

Le Théorème de Riemann-Roch

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.)

Masur-Veech Volumes of the Moduli Space of Abelian Differentials

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.)

Undergraduate notes
Lie Groups, Lie Algebras, and Representation Theory

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.)

Mathematical Analysis

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.

Solutions of Algebra: Chapter 0 by P. Aluffi

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.

Solutions of Real and Complex Analysis by W. Rudin

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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