Yuri Santos Rego

Dr. Yuri Santos Rego

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

I am a postdoc (wissenschaftlicher Mitarbeiter,  ≈ research assistant) in the Geometry Group of Prof. Petra Schwer at the Otto-von-Guericke Universität Magdeburg.

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

My research concerns properties of spaces and of their symmetries. 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" (i.e. "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, and combinatorial aspects of groups and spaces on which they act.

Groups that I like include (but are not limited to) matrix groups (algebraic, Lie, (S-)arithmetic,...), R. Thompson's groups and their relatives, locally compact groups, and Artin-Tits groups. In the topological realm I also enjoy things like knots and links 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 am also puzzled by Costas arrays.


Research papers

  • Twisted conjugacy in soluble arithmetic groups (joint with Paula Macedo Lins de Araujo), preprint, 2020. arXiv:2007.02988
  • On the finiteness length of some soluble linear groups, preprint, 2019. arXiv:1901.06704
  • Split-braid-merge diagrams, 3-manifolds, and conjugacy in a braided Thompson group (joint with Kai-Uwe Bux), preprint, 2018.
  • Presentations of parabolics in some elementary Chevalley-Demazure groups, preprint, 2018. arXiv:1801.05320
  • Formalization in PVS of balancing properties necessary for proving security of the Dolev-Yao cascade protocol model (joint with Maurício Ayala-Rincón), Journal of Formalized Reasoning, vol. 6, no. 1, 2013, 31--61. (pdf, full PVS theory: PVS 5.n, PVS 6.0)

Further written academic work

  • Arithmetic groups and Reidemeister classes, extended abstract, to appear in: "Geometric structures in group theory" [Bridson, M., Druțu, C., Kramer, L., Rémy, B., Schwer, P. (orgs.)], Oberwolfach Rep. 16/2020.
  • Finiteness properties of split extensions of linear groups, PhD thesis, Universität Bielefeld, Bielefeld, 2019. pdf
  • 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, 1579--1633. pdf
  • A desigualdade de Golod-Šafarevič para grupos pro-p e grupos abstratos, Master's dissertation, Unicamp, Campinas, 2014. (pdf, 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)

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

Recently 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 the event about the 25 Years of the PETMAT/UnB, organized by Prof. Luciana Ávila Rodrigues and the current students of the PETMAT.

The previous Buildings Conference (2019) took place here in Magdeburg, organized by Petra and myself.

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.

Upcoming (?) events:

Due to the current Corona Pandemic, few work trips (at least in Maths) can be scheduled. In turn, multiple online events are taking place worldwide.

I take the opportunity to urge everyone to follow the recommendations from their local health authorities (such as the Robert-Koch-Institut here in Germany) and let's do our best to fight the pandemic. Flatten the curve, be responsible, be compassionate, and stay healthy!

Recent talks:

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

Work trips:

In recent times I might have been spotted at the following events:


In der Vergangenheit war ich Tutor für die Vorlesungen Lineare Algebra für Physik und Gruppentheorie in Bielefeld sowie für die Kurse Cálculo 1, Cálculo 3, Introdução à álgebra linear, Álgebra 2, Álgebra 3 und Análise 1 in Brasília. Hier an der OvGU leite ich verschiedene Übungsgruppen und/oder (ko-)betreue Seminare und Bachelorarbeiten.

Im aktuellen Semester bin ich mit folgenden Lehrveranstaltungen beschäftigt. Weitere Infos zu den Vorlesungen bzw. Übungsgruppen finden Sie auf den entsprechenden Seiten des IAG.

Last Modification: 01.12.2020 - Contact Person: Dr. Yuri Santos Rego