Research Interests
My research is focused on algebra, particularly group theory and Lie algebras. Here are a few topics that I am usually thinking about:
Combinatorial and geometric group theory.
Finiteness properties of groups and Lie algebras (e.g. finite presentability, type FPn, BNSR-invariants).
Constructions of homological nature: non-abelian tensor products, Sidki's construction, ...
Gröbner-Shirshov bases.
Generalized torsion.
Publications
Generalized torsion elements in infinite groups. Joint with R. Bastos. arXiv:2411.17918
Compact p-adic analytic groups in which centralizers are abelian. Joint with T.S. Weigel and T. Zapata. arXiv:2411.03880
Some applications of Gröbner-Shirshov bases to Lie algebras. J. Pure Appl. Algebra 229 (2025), no. 1, Paper No. 107773, 14. DOI; arXiv:2310.12331.
Free polynilpotent groups and the Magnus property. Joint with B. Klopsch and J.M. Petschick. Forum Math. 35 (2023), no 2 p. 573-590. DOI, arXiv:2208.13691;
On the Bieri-Neumann-Strebel-Renz Σ-invariants of the Bestvina-Brady groups. Joint with D.H. Kochloukova. Forum Math. 34 (2022), no. 3, 605–626. DOI, arXiv:2010.03689;
Weak commutativity for pro-p groups. Joint with D.H. Kochloukova. Monatsh. Math. 194 (2021), no. 3, 555–575. DOI, arXiv:1910.14123;
Weak commutativity and nilpotency. J. Algebra 564 (2020), 276–299. DOI, arXiv:2001.06903;
The weak commutativity construction for Lie algebras. J. Algebra 529 (2019), 145–173. DOI, arXiv:1808.10303;
On the Σ-invariants of wreath products, Pacific J. Math. 298 (2019), no. 1, 113–139. DOI, arXiv:1709.06303.