Dr. Lucas Corrêa Lopes
About Me
I am a mathematician. I was a Ph.D. student at University of Brasília (UnB) under the supervision of Dr. Pavel Zalesski with a research period at University of Milano-Bicocca under the supervision of Dr. Thomas Weigel. I completed my Ph.D. in April 2026. My Erdős number is 4.
Currently I am a postdoctoral researcher at Federal University of Minas Gerais.
Research Interests
- Profinite groups, profinite Bass-Serre theory, geometric group theory, block theory for profinite groups.
Papers
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Lucas C. Lopes, Pavel Shumyatsky & Pavel A. Zalesskii (2024) Profinite groups with abelian Sylow subgroups, Communications in Algebra, DOI: 10.1080/00927872.2023.2239352.
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Lucas C. Lopes & Pavel A. Zalesskii (2025) Prosoluble subgroups of the profinite completion of the fundamental group of compact 3-manifolds, Journal of the London Mathematical Society, DOI: 10.1112/jlms.70330.
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Simone Blumer, Julian Feuerpfeil, Lucas C. Lopes, Claudio Quadrelli (2026+). A cohomological translation of the Kaplansky radical for profinite groups. Available on arxiv.
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(Temporary title) Pro-C subgroups of free profinite products and profinite groups acting on profinite trees (joint with P. Zalesskii): soon.
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(Temporary title) Frattini cover of PSL_2(q) (joint with T. Weigel): in preparation.
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(Temporary title) On the Magnus property for profinite groups (joint with G. M. L. Andrade): in preparation.
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(Temporary title) On the profinite completion of graph braid groups: in preparation.
My coauthors
Simone Blumer (Milan, ITA), Julian Fuerpfeil (Milan, ITA & Besançon, FRA), Claudio Quadrelli (Como, ITA), Pavel Zalesski (Brasilia, BRA), Pavel Shumyatsky (Brasilia, BRA).
Writings
- My doctoral thesis: Profinite groups acting acylindrically on profinite trees.
Book Recommendations
Starting your undergrad? Here are some books that shaped the beginning of my academic career:
- Abstract Algebra (Dummit & Foot).
- Examples of Groups (Weinstein).
- Field and Galois Theory (Morandi).
- Principles of Mathematical Analysis (Rudin).
- Real Mathematical Analysis (Pugh).
- Linear Algebra and Its Applications (Lax).
- General Topology (Willard).
- An Introduction to Algebraic Topology (Rotman).
If you are interested in learn the fundamentals for the profinite Bass-Serre theory, I suggest you to follow the short sequence:
Teaching
- Calculus 1: 2024-2025 at Universidade de Brasília
Mathematics around the world
Universidade de São Paulo
Universidade Federal de Minas Gerais
Università degli Studi dell'Insubria
Università degli Studi di Firenze
Università degli Studi di Milano-Bicocca
Universidade de Brasília