HNN extensions can be used as a way to produce a more complicated group from a simpler one, they do this by "folding" a part of the simpler group onto itself. These can, but do not necessarily, produce wild algorithmic properties. For instance, it is known that the submonoid membership problem for HNN extensions of free groups is undecidable in general. This raises the question of which HNN extensions of free groups do have decidable submonoid membership problem.

A monoid is said to be right noetherian if all of its right congruences are finitely generated.  An intriguing open question is whether every right noetherian monoid is finitely generated.  In this talk, we will survey progress on this problem, with particular focus on recent developments in the cancellative case.  

This a scientific meeting gathering researchers, PhD students, master students and undergraduate students about the recent advances in quantitative recurrence for dynamical systems. There will be two talks with plenty of discussion.

Schedule:

Alex Genaro 14:30-15:10 Title: A Counting Problem for a Symbolic System with Digit Density

Discussion period: 15:10-15:30

Coffee Break: 15:30-16:00

Gustavo Pessil: 16:00 - 16:45 Title: Dimensional complexity in non-smooth dynamics

Discussion period: 16:45-17:00

In this talk, we will present the bijective correspondence between Young diagrams and proper numerical sets. Then we will use this correspondence to introduce Young diagram decompositions for symmetric numerical sets (and semigroups). We will extend these decompositions to almost symmetric numerical semigroups.

There will be a coffee break after the seminar. 

References

In this talk I will present recent results on the descriptional complexity of basic operations on regular languages using 1-limited automata, a restricted version of one-tape Turing machines. When simulating operations on deterministic finite automata with deterministic 1-limited automata, the sizes of the resulting devices are polynomial in the sizes of the simulated machines.

In this talk I will present recent results on the descriptional complexity of basic operations on regular languages using 1-limited automata, a restricted version of one-tape Turing machines. When simulating operations on deterministic finite automata with deterministic 1-limited automata, the sizes of the resulting devices are polynomial in the sizes of the simulated machines.

In this talk we present some properties of generalized torsion elements in groups. We describe the set of generalized torsion elements in finitely generated abelian-by-finite groups. In addition, we present a family of Bieberbach groups in which every element is a generalized torsion element. This presentation is mainly based in the following papers [1,2,3]. 

There will be a coffee break after the seminar.

References

[1] R. Bastos and L. Mendonça. Generalized torsion elements in infinite groups. arXiv:2411.17918 [math.GR]. 

Given a set of generators of a finite semigroup, a natural way to show that a given element belongs to the semigroup is to provide a product of generators that is equal to this element. The minimum k such that for every set of generators and every element a product of length at most k is enough to prove membership is called the diameter of a semigroup.

In this talk, I will present recent results, obtained in collaboration with Valérie Berthé and Dominique Perrin, on the density of rational languages under shift invariant probability measures on spaces of two-sided infinite words. This notion of density generalizes a classical notion of density studied in formal languages and automata theory. The density of a language is defined as the limit in average (if it exists) of the probability that a word of a given length  belongs to the language.

This presentation is based on joint work with P. Shumyatsky. We study the class of all finite groups in which every commutator has prime power order. A group in this class is called a CPPO-group. Our interest in this class arose from the observation that it includes, as a subclass, all finite groups in which every element has prime power order - commonly known as EPPO-groups. These were the subject of foundational work by G. Higman and M.