Most of my interest lies within topology, algebra and geometry, and their applications to classical and quantum complexity theory. I also love statistics and machine learning, both theoretical and applied, so you can find me tackling some problems in these fields now and then!
Algorithmic quantum topology: knots and 3-manifolds, quantum invariants, topological quantum computing, combinatorial group theory
Foundations of data science: topological data analysis (TDA), group invariant tasks in machine learning, manifold learning
Journal publications, papers in conferences and preprints
Compressed data structures for Heegaard splittings, with Clément Maria.
Preprint.
We suggest an efficient data structure for Heegaard splittings of closed 3-manifolds and establish polynomial time algorithms, achieving exponential gains over triangulations for some problems.
Hardness of computation of quantum invariants on 3-manifolds with restricted topology, with Clément Maria.
Extended abstract published in the proceedings of the 33rd European Symposium of Algorithms (2025). Warsaw, Poland.
An algorithm that, from an input Heegaard diagram, outputs a new manifold with the same Reshetikhin-Turaev invariant but higher Hempel distance. This implies that computational complexity of the invariants is preserved when restricted to hyperbolic manifolds with no low-genus embedded incompressible surface and presented by a strongly irreducible diagrams.
LieDetect: Detection of representation orbits of compact Lie groups from point clouds, with Raphaël Tinarrage.
In Foundations of Computational Mathematics (2025).
An algorithm for the estimation of orbits of linear representations of Lie groups from finite samples,
allowing to retrieve the precise representation as a sum of irreps.
Empirical analysis of Biding Precedent efficiency in the Brazilian Supreme Court via Similar Case Retrieval, with Raphaël Tinarrage , Lucas E. Resck, Lucas T. Gomes, Jean R. Ponciano, Jorge Poco.
In Artificial Intelligence and Law (2025).
We assess the impact of binding precedents on the workload of the Brazilian Supreme Court, through time series of similar cases, and discuss the underlying legal mechanisms.
Cost Benefit Analysis for Investments in Power Grid Resilience - A Guide, with Edson Daniel Lopes Gonçalves, Joisa Dutra, Rafael Souza. In 9th Latin American Energy Economics Meeting (ELAEE) (2024). Rio de Janeiro, Brazil.
General CBA guidelines for investments in resilience against extreme climate events.
Measuring the Power Grid Resilience: A Case Study Applied to Brazilian Distribution Companies, with Joisa Dutra, Rafael Souza, Rafael Gomes, Lucas Amaro, Camila Albertin.
In 27th International Conference on Electricity Distribution (2023). Rome, Italy.
We describe the Research and Development project with CPFL to assess their grid's resilience against extreme climate eveents.
Two-body bound
states through yukawa forces and perspectives on hydrogen and deuterium, with Moira Gresham and Alexander Shaw. In American
Journal of Physics (2021).
Numerical solutions to the two-body quantum bound state problem with Yukawa potential.
Talks and posters
05 Aug 2025
CIRM Marseille, France. Centre d'Été Mathématique de Recherche Avancée en Calcul Scientifique. Topological Quantum Computing: What Gives?
04 Jun 2025
Saclay, France. jcgeo25:Young researchers in geometry. Hardness of computing quantum invariants with restricted topology.
16 May 2025
Porquerolles, France. DataShape Workshop. Hardness of computing quantum invariants with restricted topology.
26 Mar 2025
Bordeaux, France. JNIM 2025 : Journées Nationales du GDR IFM. Poster: Hardness of computation of quantum invariants on 3-manifolds with restricted topology.
2 May 2024
Porquerolles, France. DataShape Workshop. From Fields to Topology: Constructing TQFT invariants through Physics.
31 Jan 2024
Sophia Antipolis, France. DataShape Seminar. Detection of Representation Orbits of Compact Lie Groups from Point Clouds.
31 Jul 2023
Kyoto, Japan. TDA Week.
Poster: Detection of compact Lie group representations in point clouds and image data.
16 Mar 2023
Rio de Janeiro, Brazil. Transforming the Role of International Courts and Tribunals in a New Era of Adjudication.
Debator.
09 Nov 2018
Vancouver (WA), USA. Murdock Conference.
Poster title: Simulation of bound states of dark matter through Yukawa potentials.
09 Apr 2019
Walla Walla (WA), USA. Whitman College Undergraduate Conference.
Talk title: Bound states of dark matter and their cosmological consequences.
Teaching
Sep - Dec 2023
Introduction to Mathematical Modeling Applied to Law. Direito FGV, 16 hours.
Misc
I have recently implemented a pre-calculus quiz that I used to give my Calculus student when I was a tutor at Whitman College.
I am huge fan of old video games. You can check my list of games to play (and you can use it to store yours as well).
