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2nd of June
2nd of June
10:15 - 10:30
Reception
Reception
André Carvalho and Lennart Obster
10:30 - 11:20
Towers in Dynamical Systems
Towers in Dynamical Systems
João Matias
Abstract: A successful approach in Dynamical Systems consists in using inducing schemes with certain recurrence rates to deduce statistical properties such as the existence of invariant measures, decay of correlations or large deviations. In this approach, two types of schemes have been used: Gibbs-Markov structures and Young structures (commonly known as Young Towers). These structures are highly nontrivial and a natural question consists in knowing to what extent this approach can be applied.In this talk, we begin by giving basic notions and results from Ergodic Theory that motivate the study of these inducing schemes. Later, we will define the structures and present some of the results we can obtain from them. Finally, if time allows, we will discuss the problem we are currently working on, regarding the existence of Young Structures with certain recurrence rates.
11:30 - 12:30
On counting numerical semigroups
On counting numerical semigroups
Neeraj Kumar
Abstract: Numerical semigroups are the cofinite submonoids of the natural numbers. We discuss the notion of counting numerical semigroups through their different invariants (such as the genus and the Frobenius number), along with the key problems associated with them. Then we introduce a new way of counting, namely by fixing the maximum generator of a semigroup, and discuss its properties and relation with the already existing ways of counting.Lunch 12:30 - 14:00
14:00 - 14:50
Eldeman-Greene insertion
Eldeman-Greene insertion
Diogo Soares
Abstract: In 1984, Richard Stanley computed for the first time the number of reduced decompositions for the reverse permutation $w_0$. He used generating functions to show that the number of reduced decompostions of $w_0$ is equinumerous to the number of standart Young tableaux of staircase shape. Three years later, Eldeman and Greene gave a bijective proof of Stanley’s result using a variation of the RSK insertion algorithm. In this talk we explore the Eldeman-Greene insertion with some recent results involving this algorithm.Break 14:50 - 15:00
15:00 - 15:50
Descent theory for categorical structures
Descent theory for categorical structures
Rui Prezado
Abstract: Effective descent morphisms are the fundamental notion in the study of Janelidze-Galois theory and Grothendieck descent theory, and providing descriptions of such morphisms in a category of interest C makes the tools from those fields available to use in studying C. After reviewing this notion of effective descent morphism, we will discuss the current state of descent theory for categories of categorical structures.Break 15:50 - 16:00
16:00 - 16:50
Compatible Lie algebras
Bernardo Cunha
Abstract: In this talk we will briefly recall the notion of Lie algebra, before moving on to the concept of a compatible Lie algebra, which is a generalisation consisting of an algebra with two Lie products, satisfying a certain compatibility condition. We introduce many definitions and discuss some results which are analogous to the non compatible case, ranging from cohomology to nilpotence.Coffee Break
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