# Thiago Brevidelli Garcia

## Stuff I wrote

Lie Algebras & their Representations

My undergraduate dissertation on the representation theory of Lie algebras, with an emphasis in the classification of irreducible representations of finite-dimensional semisimple Lie algebras (PDF)

Notes on representation theory (under construction)

My personal thoughts on representation theory (of groups and Lie algebras) — which is what I currently study — with an emphasis in the beautiful interplay between the algebraic and the geometric (PDF)

Global Analysis & the Banach Manifold of Class ${H}^{1}$ Curves

Riemannian Geometry course project on the manifold ${H}^{1}\left(I,M\right)$ of class ${H}^{1}$ curves on a Riemannian manifold $M$ and its applications to the geodesics problem. (PDF)

Forcing in Topos (Portuguese)

Set Theory course project (with Gabriel Bassan, Guilherme Sobreira and Guilherme Cerqueira) on Lawvere’s formulation of Cohen’s forcing method in the context of elementary topoi (PDF)

An essay on the 3-sphere and some its quotients

Short notes on the 3-dimensional sphere, its group structure and some of its quotients by finite subgroups of its center, such as the projective space ${ℝ\text{P}}^{3}$ (PDF)

## Past talks

The PBW Theorem

Vertex Algebras course project at IMPA, February 2023

Vertex Algebras course project on Braverman's and Gaitsgory's proof of the PBW theorem for quadratic Koszul algebras (Slides)

Infinite-Dimensional Geometry & Ideal Fluids

Geometry & Mathematical Physics Workshop, December 2022

A seminar on the Euler equation for ideal incompressible fluids, Fréchet manifolds and the geometry of the group of volume-preserving diffeomorphisms. (Slides) (Video)

Irreducible Weight Modules (Portuguese)

Undergraduate dissertation, December 2022 (Slides) (Video)

Lie's Third Theorem (Portuguese)

Algebraic Topology course project, November 2022

A seminar on Duistermaat's proof of Lie's third fundamental theorem (the one later generalized by Marius and Ruy on their classification of integrable Lie algebroids)

Representations of Lie Groups and Algebras (Portuguese)

30th SIICUSP, October 2022 (Slides)

How to prove theorems in a computer? (Portuguese)

S4 Seminar, October 2022 (Slides)

Lie Theory or: why study Lie algebras? (Portuguese)

CFuD Seminar, April 2022

Who are the p-adic integers anyway? (Portuguese)

S4 Seminar, November 2021 (Slides) (Video)

How to do Mathematics in a Computer? (Portuguese)

S4 Seminar, August 2021 (Slides) (Video)

Representations of Compact Groups: What? Why? How? (Portuguese)

Study seminar RTAG, July 2021 (Slides)

When is something equal to something else? (Portuguese)

S4 Seminar, April 2021 (Slides)

Lecture on the idea of isomorphisms and invariants throughout mathematics

How to do algebra with analysis? (Portuguese)

Shokugeki Seminar, March 2021 (Slides)

On Pontryagin duality

The Monster Group (Portuguese)

Shokugeki Seminar, February 2021 (Slides)