Por Pedro Filipe (Instituto Superior Técnico, Universidade de Lisboa).

Abstract: The compactness theorem is one of the key ingredients used in Lindstrom's Theorem that characterizes first-order logic and follows directly from Godel's completeness theorem, given the finite nature of proofs. In time, alternative proofs were found that don't require the usage of a formal proof system. In this seminar we will show one of these alternative proofs using ultrafilters and ultraproducts.

Exposição patente ao público até 31 de março de 2019 (dias úteis, 08h00 às 19h30).

Esta mostra surge como um breve olhar sobre algumas das aplicações da matemática na biologia, exemplos de como eliminando fronteiras se consegue ir mais longe.

Conceção e Textos: Ana Maria Eiró; António Monteiro; Carlos Albuquerque; Cristina Luís; José Francisco Rodrigues; Luís Mateus; Pedro Moura; Suzana Nápoles; Tiago Marques
Design gráfico: João Sotomayor

Por Benito Pires (Universidade de São Paulo).

Por Maurício Misquero (Universidade de Granada).

Por Harbir  Antil (George Mason University).

Por Carlos Florentino (Universidade de Lisboa, CMAFcIO).

Abstract: Generalizing the classical theory of algebraic invariants, David Mumford introduced Geometric Invariant Theory in order to endow natural quotients and moduli spaces with algebro-geometric structure. It turned out that quotients in algebraic geometry are intimately related to quotients in symplectic geometry, through the famous Kempf-Ness theorem.

Por Alfio Quarteroni (Politecnico di Milano, Italia).

Por Marcel Xavier (LNCC, Petropolis, Brasil).

Abstract: The topological derivative is a scalar field that measures the sensitivity of a given shape functional with respect to an infinitesimal singular domain perturbation, such as the insertion of holes, inclusions, source-terms or even cracks. In this work, the concept of topological derivative is applied in the context of damage and fracture mechanics. In particular, the nucleation and propagation damaging process are studied.

Por Riccardo Scala (University of Rome 1, “La Sapienza”).

Abstract: We introduce the notion of area of the graph of a smooth function and the definition of the corresponding relaxed functional. We discuss some issues related to determine the domain and the exact value of it on singular maps. Finally we show how this question is related to Plateau-type problems with mixed boundary conditions and how to solve it in some specific cases.

Por Wladimir Neves (Instituto de Matemática, Universidade Federal do Rio de Janeiro, Brasil).

Abstract: In this talk, we consider a fractional type degenerate heat equation posed in bounded domains. We show the existence of solutions for measurable and bounded non-negative initial data, and homogeneous Dirichlet boundary condition. The nonlocal diffusion effect relies on an inverse of the s-fractional Laplacian operator, and the solvability is proved for any s , 0 < s < 1.