Right-angled Artin groups (RAAGs) are fundamental objects in geometric group theory. They are defined by simplicial graphs, with generators corresponding to vertices and commutation relations determined by edges. This talk introduces twisted right-angled Artin groups (T-RAAGs), a natural extension of RAAGs constructed from mixed graphs that include both undirected and directed edges. Undirected edges impose the usual commutation relations (ab = ba), while directed edges introduce Klein-type relations of the form (aba = b).

Quasi-Frobenius rings were introduced by Nakayama  in the study of representations of algebras. Afterwards, Quasi-Frobenius rings played a central role in ring theory, and numerous characterizations were given by various authors. In particular, Ikeda characterized these rings as two sided self-injective and two sided Artinian.

Given a topologically mixing shift on a countable alphabet and a potential, we give criteria for the system to have exponential mixing.  That is, criteria for the potential to have an equilibrium state which also has exponential decay of correlations.  The first condition is that the potential should have Birkhoff averages on periodic points bounded away from its pressure.  The second is that we control the entropy at infinity.  Both conditions are sharp (in fact under the second condition, the first is both necessary and sufficient).  I will present this joint work with Boyuan Zhao using s

Using a deterministic perturbation result established by Galatolo and Lucena [1], we obtain quantitative estimates on the continuity of the invariant densities and entropies of the physical measures for a one parameter family of piecewise expanding maps. We apply these results to a family of two-dimensional tent maps.

[1] S. Galatolo, R. Lucena, Spectral gap and quantitative statistical stability for systems with contracting fibers and Lorenz-like maps, Discrete and Continuous Dynamical Systems 40, 3 (2020), 1309--1360

The membership problem for algebraic structures asks whether a given element belongs to a specific substructure, typically defined by a set of generators. For finite semigroups this problem has been shown to be PSPACE-complete in the transformation model (Kozen, 1977) and NL-complete in the Cayley table model (Jones, Lien, and Laaser, 1976). More recently, the membership and conjugacy problems for finite inverse semigroups were also found to be PSPACE-complete in the partial bijection model (Jack, 2023).

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:

Romain Aimino 14:30-15:10 Title: Records for dynamical systems

Discussion period: 15:10-15:30

Coffee Break: 15:30-16:00

Jorge Freitas: 16:00 - 16:45

Discussion period: 16:45-17:00

Title: Totally positive skew-symmetric matrices

The main objective of multiplicative ideal theory is to investigate the multiplicative structure of integral domains by means of ideals or certain systems of ideals of that domain. An essential tool in multiplicative ideal theory is the concept of  ``star operation"  which was introduced by Krull in 1936 and then was used by Gilmer in his book in 1972. In this talk, we first introduce some concepts related to multiplicative ideal theory. The emphasis will be given to the ``$w$-operation", one of the most important star operations.

In this talk, we will investigate the question of quantitative recurrence for ergodic dynamical systems. By fixing a set of small measure in phase space, we study the law of successive return times to this target as the measure tends to zero. When the invariant measure is finite and the system is sufficiently mixing, it is known that the limit law obtained for natural targets (typically balls or cylinders) is the Poisson process. In this presentation, we will focus on the case where the invariant measure is infinite.

In this talk, I will explore the connection between algebraic language theory and topos theory, focusing on why algebraic language theory is appealing to topos theorists—or at least to me. I will begin by introducing toposes as a simultaneous generalization of topological spaces and monoids. Then, I will construct the topos of automata, the topos of regular languages, and the toposes of other language classes. Finally, I will discuss what topos theory might offer to automaton theory, particularly in relation to “geometric invariants” in topos theory.