Por Luigi Santocanale (Aix-Marseille Université).

The set of permutations on a finite set can be given the lattice structure known as the weak Bruhat order.

Professor Mária B. Szendrei is world recognized leader on the theory of regular semigroups and their generalization. Her research develops and deepens several classic directions in studying various classes of regular semigroups; at the same time, she has invented many novel and inherently original approaches that opened new avenues of research.

Por Filipa Soares (ISEL-IPL, CEMAT-Ciências).

Resumo: Neste seminário iremos estudar uma noção que se situa entre a de variedade localmente finita e a de variedade periódica, chamada variedade localmente K-finita, onde K é uma das cinco relações de Green. Mais precisamente, diz-se que uma variedade é localmente K-finita se, nela, todo o semigrupo finitamente gerado tem um número finito de K-classes. Iremos descrever as caracterizações obtidas, todas elas formuladas na linguagem de "objetos proibidos".

Por Célia Borlido (Laboratoire J. A. Dieudonné, CNRS, Université Côte d'Azur).

Por Lucía Suárez (ISEL/IPL).

Por Bernardo Fernandes (DM | FCUL e CEMAT-Ciências).

Por Peter J. Cameron (Univ. St Andrews e CEMAT).

Abstract: The Coxeter--Dynkin diagrams of type ADE occur in so many different parts of mathematics, from singularity theory to mathematical physics to graph theory, that they surely play a very deep role in our subject. In the present century, they have occurred in the theory of cluster algebras by Fomin and Zelevinsky, and a constructive version of the McKay correspondence has been found by Dechant. The talk will discuss some of these connections.

Por Mário Branco (Ciências-ULisboa e CEMAT).

Por Jean-Éric Pin (Institut de Recherche en Informatique Fondamentale, CNRS et University Paris-Diderot).

Abstract: Difference hierarchies were originally introduced by Hausdorff and they play an important role in descriptive set theory. In this lecture, I will review standard techniques on difference hierarchies, mostly due to Hausdorff. These techniques will be illustrated by some decidability results on difference hierarchies based on shuffle ideals and polynomials of group languages.