Conjugacy languages, first introduced by Ciobanu and Hermiller, are a useful tool in understanding the behaviour of conjugacy classes in finitely generated groups. In this talk I will survey what we know so far about two of these languages, namely the conjugacy geodesic language, and the shortlex conjugacy language. We will discuss some algebraic and geometric techniques that can be used to determine the nature of these languages in different groups.

The specification property, introduced in the 1970s by Bowen in the study of Axiom A diffeomorphisms, is a fundamental tool in dynamical systems and it is closely related to chaotic behavior and rich ergodic properties. Although important classes of systems have the specification property, several relevant classes of systems do not have it, and therefore, weaker notions we introduced, such as the weak and almost specification properties.

In the previous talk, we revisited some general aspects of the representation theory of the Lie algebra $\mathrm{gl}(n)$ and used them as motivation to study Gelfand-Tsetlin modules via Drinfeld categories. In this seminar, we will take a step back to build a solid foundation before diving into Gelfand-Tsetlin modules. We will start by recalling key results from the classical representation theory of $\mathrm{sl}(2)$, ensuring that we have the necessary tools and intuition. With this groundwork in place, we will then explore how Gelfand-Tsetlin modules appear in this setting.

We introduce an algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. An initial implementation of this algorithm outperforms existing implementations by several orders of magnitude. Joint work with Luna Elliott and James Mitchell.

I will discuss the outcome  of  periodic perturbations of attracting cyclic dynamics.  
The system to be perturbed may be either a periodic orbit, a heteroclinic cycle or a flow-invariant torus. 
We look for frequency locked solutions that return after an integer multiple of the period of the perturbation.
The analysis consists in reducing to discrete-time dynamics on a cylinder and the golden number has a surprise participation.

This is joint work with Alexandre Rodrigues (ISEG, U. Lisboa).

In this talk, we will focus on formations and Fitting classes of groups. A formation of groups is a class of groups closed under quotients and subdirect products of finite families, while a Fitting class of groups is a class of groups closed under normal subgroups and products of two normal subgroups belonging to the class.

In [1], different definitions of the product of classes of groups have been presented, and studied, particularly regarding the preservation of properties as being a formation or a Fitting class.

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:

Mubarak Muhammad 14:00-14:30 Title: Trimmed sums for slowly mixing systems

Discussion period: 14:30-15:00

Coffee Break: 15:00-15:30

Duarte Sá Pinho: 15:30 - 16:00 Title: Extremal index for bidimensional systems

Discussion period: 16:30-16:30

Let $\mathcal{C}\subseteq\mathbb{N}^p$ (for a non-zero natural number $p$) be a non-negative integer cone. A monoid $S \subseteq \mathcal{C}$ is called a $\mathcal{C}$-semigroup if its complement in the cone is finite. This structure naturally extends the classical notion of numerical semigroups, which are submonoids of the natural numbers with a finite complement in the set of natural numbers.

Nos últimos anos, houve um grande interesse em detectar propriedades do grupo fundamental $\pi_1(M)$ de uma $3$-variedade por meio de seus quocientes finitos ou, mais conceitualmente, pelo seu completamento profinito. Isso motiva o estudo do completamento profinito $\widehat{\pi_1(M)}$ do grupo fundamental de uma $3$-variedade. Um trabalho recente de 2017 de H. Wilton e P. Zalesskii mostra que as decomposições típicas de grupos de $3$-variedades, como produtos livres com amalgamação, extensões HNN e grafos de grupos, são preservadas sob o completamento profinito.

In this talk, extensions of solvable Lie algebras are considered. The method of central extension is mostly used to obtain a classification of nilpotent algebras. This method was generalized for the solvable Lie algebras by T. Sund in 1979. We investigate extensions of solvable Lie algebras with naturally graded filiform nilradicals. Moreover, we generalize this method for the solvable Leibniz algebras and find extensions of solvable Lie algebras with null-filiform and filiform nilradicals.