Undergrad Projects

Most of the contents below are in portuguese.

I am proud to have been an organizer of the S4 student seminar group at IME-USP, which aims to present interesting topics and ideas in math to undergraduate students. Here is a link to some past seminars on Youtube.

• Presentation on supermanifolds for my Topics in Mathematical Physics class. Here is a video of the presentation, but the audio is terrible :(
• A note on the Sasaki metric and the proof that the geodesic flow.
• Presentation on differential forms and de Rham Cohomology.
• Classification of (triangulated) surfaces.
• Presentation on Riemann surfaces and Pick's theorem.
• Presentation on Hubbard Trees.
• Presentation on the connectivity of the Mandelbrot Set.
• A note on the \(3\)-sphere.
• Written version of a group project on small cardinais.
• Group activity problem we created at the 2020 CIIM. If you want to tackle it, feel free to email me your solution!
• A minor generalization of the theorem on tangent bifurcations in one-dimensional dynamics.
• An elementary analysis of the \( C^r \) distance of functions on compact sets of the real line and minor applications to structural stability.
• Some notes on "number-less" induction that arose from fruitful conversations with Prof. Odilon Otávio Luciano. Two followup texts were this one and this one.

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