Recent Projects

Thurston Theory

• An alternative proof of Thurston's topological criterion, via an object called the Rees Space. Also, expanded (unfinished) notes on the Rees space.
• A proof that polynomial-like, critically periodic Thurston maps are unobstructed.
• Calculation of an asymptotic lower bound for the smallest possible geodesic during an unobstructed Thurston iteration.

Complex Dynamics

• Slides on an algorithm that encodes the set of external rays landing on the Hubbard tree of a PCF polynomial as a finite state automaton; presented at the 2026 Early Career Complex Dynamics Workshop. The algorithm is available here. I hope to soon put together notes detailing a proof that the algorithm works and data gathered from it, especially in applications to matings of polynomials.
• Laminations as finite state automata (unfinished).
• Some drawings and proofs about annuli, children and quadratic Yoccoz puzzles. Also more thoughts, proofs and exercises in reference to Milnor's paper on quadratic Yoccoz puzzles.
• Solutions and thoughts on Milnor's book Dynamics in One Complex Variable.
• Introduction to holomorphic dynamics.

Complex Analysis and Geometry

• A collection of facts about extremal length and width.
• Basic results on the theory of ends.
• Introduction to the theory of quasiconformal maps.

Others

• Presentation on the theory of distributions (in portuguese).

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