Thiago Brevidelli Garcia
Welcome to my academic home page! I’m currently a mathematics student at the M2 Research & Innovation graduate program in Toulouse, France. My main interests at the moment are representation theory, specifically Lie theory, as well as differential geometry and adjacent fields.
Stuff I wrote
- Semisimple Lie Algebras & their Representations
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My notes on the representation theory of semisimple Lie algebras, with an emphasis in Olivier Mathieu's classification of simple weight modules (PDF)
- Global Analysis & the Banach Manifold of Class Curves
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Riemannian Geometry course project on the manifold of class curves on a Riemannian manifold and its applications to the geodesics problem. (PDF)
- Forcing in Topos (Portuguese)
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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
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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 (PDF)
Past talks
- Cobordism Groups & the Pontryagin Construction
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MINT inverted class at IMT, November 2023
MINT inverted class course project on a proof of the fact that the Pontryagin construction yields an isomorphism between framed cobordism groups and higher homotopy groups of spheres (Slides)
- The PBW Theorem
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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
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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)
- Lie's Third Theorem (Portuguese)
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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)
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30th SIICUSP, October 2022 (Slides)
- How to prove theorems in a computer? (Portuguese)
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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)
- How to do Mathematics in a Computer? (Portuguese)
- Representations of Compact Groups: What? Why? How? (Portuguese)
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Study seminar RTAG, July 2021 (Slides)
- When is something equal to something else? (Portuguese)
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S4 Seminar, April 2021 (Slides)
Lecture on the idea of isomorphisms and invariants throughout mathematics
- How to do algebra with analysis? (Portuguese)
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Shokugeki Seminar, March 2021 (Slides)
On Pontryagin duality
- The Monster Group (Portuguese)
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Shokugeki Seminar, February 2021 (Slides)