The COVID pandemic is still conditioning CIM’s activities and, in
particular, some events partially supported by CIM occurred online.
Symbolic powers arise naturally in commutative algebra from the theory of primary decomposition, but they also contain geometric information, thanks to a classical result of Zariski and Nagata. Computing primary decompositions is a difficult computational problem, and as a result, many natural questions about symbolic powers remain wide open. We will briefly introduce symbolic powers and describe some of the main open problems on the subject, and point to some recent research advances.
Adélia Sequeira (https://www.math.tecnico.ulisboa.pt/~asequeir/) was born in Lisbon on 14 March, 1951. She is a Full Professor of Mathematics at the IST (Instituto Superior Técnico), Universidade de Lisboa, was Director of the Research Centre for Computational and Stochastic Mathematics — CEMAT/IST-ULisboa (2017–2021) and has been the Scientific Coordinator of CEMAT’s Mathematical Modeling in Biomedicine Research Group (since 2010).
On the 26th of November of 2021, the Workshop CIM & Enterprises was held virtually. It was promoted and organized by CIM, the International Center for Mathematics, in collaboration with PT-MATHS-IN, the Portuguese Network of Mathematics for Industry and Innovation.
Hugo Baptista Ribeiro was a distinguished portuguese mathematician who made part of the Geração de 40, a generation of mathematicans which was responsible for renewal of Mathematics in Portugal in the decade 1936–1945. Members of this group were Bento de Jesus Caraça, Ruy Luis Gomes, António Aniceto Monteiro, Manuel Zaluar Nunes and others.
Elliptic partial differential equations are a very import class of equations with obvious connections to applied sciences (e.g. physics, biology, chemistry and engineering) as well as to other fields of Mathematics such as Differential Geometry, Functional Analysis and Calculus of Variations. Because of these facts they are a quite fascinating topic and an increasingly active field of research. In this article we focus our attention on semilinear problems of type Delta u = f(u), more specifically on the Lane-Emden equation, as a mean to explain some of the tools and methods (mostly topological or variational) that are available to treat elliptic problems. The topics addressed concern existence and multiplicity of solutions, as well as their qualitative properties such as sign and symmetry.
International Conference On the occasion of Andrey Sarychev’s 65th birthday, University of Aveiro, February 3–5, 2021
The Tipografia Matemática Portuguesa: 1496–1987 is a unique, rare and eloquent exhibition, which first edition took place from July 1st to October 31st 2021 in the hexacentenary Moinho de Papel in Leiria, a city with an ancient castle since the 12th century in the center of Portugal, residence of kings and setting of several cortes (medieval parliaments). The city gave the name to a famous pine forest (Pinhal de Leiria), wood supplier of the ships used in the Portuguese navigations of the 15th and 16th centuries. The exhibition was an initiative of the city of Leiria in partnership with the CIM and the Polytechnic Institute of Leiria.
One of the aftermaths due to the pandemic crisis was the revocation of the Encontro Nacional da SPM (ENSPM) 2020 that should have been done in the beautiful city of Tomar, in July 2020. After advances and setbacks and numerous doubts faced by the newly elected directive board of the SPM, in September 2020, finally it was established that 2021 would not end without a remarkable ENSPM!
Given a compact connected Lie group G and a closed manifold M it is natural to ask if M admits a nontrivial action of G and, if yes, how many different actions it can have. The existence of even the simplest case of a circle action already imposes strong restrictions on the topology of the manifold. We will explore some of these restrictions, illustrating how the simple existence of a circle symmetry already provides much information on the underlying manifold.