Yuri Santos Rego

Dr. Yuri Santos Rego

Institut für Algebra und Geometrie (IAG)
Geometry Group & MathCoRe
Universitätsplatz 2, 39106 Magdeburg, G03-220a
Sprechzeiten: by appointment (by e-mail or in person)

I am a wissenschaftlicher Mitarbeiter (≈ research assistant) in the Geometry Group of Prof. Petra Schwer, associated fellow of the GRK2297 "Mathematical Complexity Reduction" (MathCoRe), and researcher in the SPP2026 "Geometry at Infinity".

I got my PhD from the Universität Bielefeld under the supervision of Prof. Kai-Uwe Bux. Before that I got my Master's degree from the Universidade Estadual de Campinas (Unicamp), advised by Prof. Dessislava Kochloukova, and my Bachelor degree from the Universidade de Brasília (UnB). In Brasília I was also a member of the groups PETMat-UnB and Theory of Computation under the guidance of Profs. Mauro Rabelo and Maurício Ayala-Rincón, respectively.

Research interests

I am an algebraist by training and a topologist/geometer in spirit, which means I work in group theory. That is, my research concerns properties of spaces and of their symmetries (such as reflections). The fun part is that the term "space" can be interpreted quite broadly, from a hairy ball to a comic-book-like multiverse known as Bruhat--Tits building, from fundamental geometric shapes to model spaces describing the motion of a robot.

In this area one can investigate a wide variety of problems. For example, regarding the space we could ask whether there exist serious obstructions in it (such as holes of various dimensions), whether it is curved somehow, what happens when we move "forever" (e.g., "towards infinity"), or whether we can describe what happens over time with an object moving in the given space under certain rules.

As for the symmetries themselves, we might want to know for instance how many there are, whether we can describe them in a simple fashion, how they transform objects in the given space, whether there are points left unchanged by the symmetries, or about the relationship between given sets of symmetries of two spaces (possibly even the same!).

In more technical terms, my work so far has been mostly in combinatorial/geometric group theory and related topics from topology. I had/have particular interest in presentations, (cohomological) finiteness conditions, Reidemeister classes, and algorithmic questions. As such, I am very fond of geometric, topological, homological, combinatorial, and algorithmic aspects of groups and spaces on which they act.

Groups that I like include (but are not limited to) linear groups (algebraic and Lie groups, their (S-)arithmetic counterparts, Coxeter groups, ...), R. Thompson's groups and their relatives, and locally compact (including profinite) groups. In the topological realm I also enjoy things like knots and links (and more generally spatial graphs) and questions about low-dimensional spaces.

As a former member of the group of Theory of Compuation in Brasília, I am also interested in formal methods in mathematics and proof assistants. I recent times I have also been puzzled by Costas arrays.


Research papers

Further written academic work

  • Arithmetic groups and Reidemeister classes, extended abstract, in: "Geometric structures in group theory" [Bridson, M., Druțu, C., Kramer, L., Rémy, B., Schwer, P. (orgs.)], Oberwolfach Rep., vol 17, no. 2 / 3, 2020, 900--903. (journal)
  • Finiteness properties of split extensions of linear groups, PhD thesis, Universität Bielefeld, Bielefeld, 2019. (DOI:10.4119/unibi/2937569)
  • Spraiges, 3-manifolds, and conjugacy for a braided Thompson group, extended abstract, in: "Cohomological and metric properties of groups of homeomorphism of R" [Burillo, J., Bux, K.-U., Nucinkis, B. E. A. (orgs.)], Oberwolfach Rep., vol. 15, no. 2, 2018, 1594--1598. (journal)
  • A desigualdade de Golod--Šafarevič para grupos pro-p e grupos abstratos, Master's dissertation, Unicamp, Campinas, 2014. (DOI:10.47749/T/UNICAMP.2014.932005, in Portuguese)
  • Vivências matemáticas (joint with Paula Macedo Lins de Araujo and Mauro Luiz Rabelo), in: Anais do II EnaPETMAT, pp. 7, Universidade Federal do Goiás (UFG), Goiânia, 2010. (pdf, in Portuguese)
What's on (or was)

I organized the last meeting of the 'Thompson community', namely the GoTh Workshop: Thompson groups and their relatives, jointly with Kai-Uwe Bux, Ilaria Castellano and José Pedro Quintanilha. The event took place in September 2023 here in Magdeburg, gathering over 50 participants among long-time experts, newcomers, and enthusiasts from all around the globe. Thanks for joining!

The Young Geometric Group Theory XI (2023) took place in Münster, organized by Giles Gardam, Kasia Jankiewicz, Bakul Sathaye, and myself. We hosted over 150 participants from 16 countries. Thanks for joining!!
Our grants (from the SPP 2026, the Excellence Cluster in Münster, the MathCoRe here in Magdeburg and the US american NSF) covered most of the costs.
At the YGGT XI I was also appointed as a Panelist for the "Equity, Diversity, and Inclusion" (EDI) Panel, together with Indira Chatterji, Alex Edletzberger and Genevieve Walsh.

Anna Michael, Felix Reinbott and I organized the Annual Colloquium 2022 of the MathCoRe, which took place in Thale. We also hosted there a special session about "Maths, Geopolitics, and Society", jointly with Barbara Witter.

The Buildings Conference Series, previously organized by Linus Kramer, moved to Magdeburg in 2019 after a long time -- it was then organized by Petra and myself. Its sequel, the Buildings 2021, also took place here in Magdeburg, organized by Anna Michael, Isobel Davies, Petra Schwer and myself.

At the OvGU I founded the WISST! - das "What is..."-Seminar beim Tee!, where we get to learn new stuff from Maths and Didactics in an informal environment.

In 2020 I shared a few words about my academic path so far and the importance and meaning of the PETMAT Program in Brasília. The (online) meeting was part of an event on the 25 Years of the PETMAT/UnB, organized by Prof. Luciana Ávila Rodrigues and the current students of the PETMAT. Prof. Ávila Rodrigues published a book (open access, downloadable here) about the history of this successful program, and my brief testimony was published in the book (p. 203; in Portuguese).

The IAG runs a joint Oberseminar, check out its homepage for announcements and program.
From the WiSe2017/2018 to the WiSe2018/19 I was also co-organizer of the Oberseminar Gruppen und Geometrie in Bielefeld.

In June 2018 I served as a reporter for the Oberwolfach Workshop on Cohomological and metric properties of groups of homeomorphisms of R.

Together with Benjamin Brück and Eduard Schesler I organized the Block Seminar on Arithmetic groups and rigidity, which took take place in Bielefeld in March 2018. The most recent Block Seminar, Constructions of aspherical manifolds and complexes, was organized by our colleagues from Regensburg and took place on the Frauenchiemsee in September 2018.


Recent talks:

Outside the OvGU, you might have recently heard about my work at...

Upcoming work trips:

In the near future you might meet me at...


Here at the OvGU I give lectures, exercise classes, and supervise seminars and theses. Check out LSF to keep up to date with courses offered by our Institute. If you would like to write a Bachelor or Master's thesis in our Geometry Group, feel free to contact me!


  • Yannick Steinkamp (2020, Bachelor Informationstechnik, co-supervised with Petra Schwer) -- Gödels erster Unvollständigkeitssatz - über dessen historischen Beweis und verschiedene Verallgemeinerungen.
  • Anna Wagner (2022, Bachelor Mathematik) -- The fundamental group. Distinguishing knots via group theory.

In the past I was a Tutor for "Linear Algebra for Physics" and "Group theory" at Bielefeld, and a T.A. for "Calculus 1", "Calculus 3", "Introduction to linear algebra", "Algebra 2", "Algebra 3" and "Analysis 1" at Brasília.

In the current Semester I am responsible for the following courses. (For more information please check out the corresponding pages of the IAG.)

Last Modification: 15.09.2023 - Contact Person: Yuri Santos Rego