Undergraduate & Master's
I was an undergraduate at the Mathematics and Statistics Institute of the University of São Paulo (IME-USP). In June 2024 I concluded my Master's at the M2 Research & Innovation program from the Institut of Mathématiques de Toulouse (IMT), France. During my Master's I was a MINT Fellow.
Written Work
- Mapping Class Groups & their Representations
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My M2 Mémoire (Master's Thesis) on low-dimensional representations of the mapping class groups of surfaces (PDF)
- Semisimple Lie Algebras & their Representations
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Expanded (unfinished) version of my undergraduate thesis 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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Undergraduate Riemannian Geometry course project on the manifold of class curves on a Riemannian manifold and its applications to the geodesics problem. (PDF)
Talks
- Mapping Class Groups & their Representations
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M2 Soutenance, July 2024
Master's Thesis defense on low-dimensional representations of the mapping class groups of surfaces (Slides)
- Tate Modules
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M2RI Elliptic Curves Reading Seminar, February 2024
M2RI Elliptic Curves Reading Seminar presentation on Tate modules and their applications to the study of isogeny groups
- 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)