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

• Lucas C. Lopes, Pavel Shumyatsky & Pavel A. Zalesskii (2024) Profinite groups with abelian Sylow subgroups, Communications in Algebra, DOI: 10.1080/00927872.2023.2239352.

• 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.

• A cohomological translation of the Kaplansky radical for profinite groups (joint with S. Blumer, J. Feuerpfeil, C. Quadrelli): soon.

• (Temporary title) Frattini cover of PSL_2(q) (joint with T. Weigel): in preparation.

• (Temporary title) Pro-C subgroups of the fundamental group of acylindrical profinite graphs of profinite groups (joint with P. Zalesskii): in preparation.

Writings

• My doctoral thesis: Profinite groups acting acylindrically on profinite trees (soon).

Profinite groups, free constructions and some Bass-Serre theory:

These texts are some interesting parts of my personal notes written in preparation for my PhD Algebra Exam. I will upload the archives randomly. Unfortunatelly they are only in portuguese at the time but I will upload an english version as soon as possible :)

• Part I: something about profinite groups.
• Part II: Free vs Projective Groups.
• Part III: Free Products.
• Part IV: Amalgamated Products.
• Part V: something about HNN-extensions.
• Part VI: something about Bass-Serre theory.

Book Recommendations

If you are an undergrad student, these are some good (in my opinion) books to construct a strong mathematical base:

• Abstract Algebra:
  • Abstract Algebra (Dummit & Foot),
  • A Course in the Theory of Groups (Robinson),
  • Examples of Groups (Weinstein),
  • Field and Galois Theory (Morandi).
• Real Analysis:
  • Real Mathematical Analysis (Pugh),
  • Principles of Mathematical Analysis (Rudin),
  • Calculus on Manifolds (Spivak).
• Linear Algebra:
  • Linear Algebra and Its Applications (Lax).
• Topology:
  • General Topology (Willard).

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

XXVII Escola de Álgebra
Universidade de São Paulo

IV Workshop in Groups and Algebras
Universidade Federal de Minas Gerais

Algebra Seminar
Università degli Studi dell'Insubria

Gruppen und topologische Gruppen
Università degli Studi di Firenze

Algebra Seminar
Università degli Studi di Milano-Bicocca

Doctoral Thesis Defense
Universidade de Brasília

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