The Iberian Mathematical Meeting is a joint event of the Real Sociedad Matemática Española (RSME) and the Sociedade Portuguesa de Matemática (SPM). It aims at bringing together spanish and portuguese mathematicians in order to develop mathematical research in the future.
Former editions of the Iberian Mathematical Meeting were held in Lisbon (2007), Badajoz (2008), Braga (2010), Valladolid (2012), Aveiro (2014) and Santiago de Compostela (2016).
Following the tradition of previous meetings, the event is structured around three main scientific areas. In this edition, the scientific areas are:
In addition to the plenary conferences, specific sessions for these three areas will be held with invited speakers and some possible contributed talks. In the name of the Organizing Committee, it is a pleasure to invite you to participate in the 7º Iberian Mathematical Meeting, to be held on October 12 - 14, 2018 at the University of Évora, Portugal.
In these pages we will update all the information about the Congress and its development. We appreciate your help in disseminating this information to get together a large number of portuguese and spanish participants. Of course all mathematicians of any other nationality interested in sharing with us these days are welcome.
We look forward to seeing you in Évora.
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Daniel AbreuARI, Austrian Academy of SciencesDonoho-Logan Large Sieve Principles for Modulation and Polyanalytic Fock Spaces
The large sieve principle covers a number of far reaching analysis
techniques, mostly aimed at solving problems in analytic number theory,
but which have also found applications in a number of other mathematical
fields, like probability, numerical and signal analysis to name a few. The
terminology stems from its number theory origins,
which can be traced back to the sieve of Eratosthenes. Donoho and Logan, in one of the fundamental papers that spearheaded the modern theory of Compressed Sensing, considered L1 versions of the large sieve principle leading to deterministic guarantees for perfect reconstruction of sparse band-limited signals using convex optimization methods (L1 minimization). After an introduction to the basics of joint time-frequency analysis, I will present recent results from a collaboration with Michael Speckbacher (ARI-Vienna), where estimates for the Lp-norm of the short-time Fourier transform (STFT) for functions in modulation spaces are obtained. The estimates provide information about the concentration of a signal on a given subset of the plane, leading to deterministic guarantees for perfect reconstruction using convex optimization methods. At the technical level, since there is no proper analogue of Beurling's extremal function in the STFT setting, we introduce a new method, which rests on a combination of an argument similar to Schur's test with an extension of Seip's local reproducing formula to general Hermite windows. When the windows are Hermite functions, we obtain polyanalytic space structures, a rich hierarchy of function spaces of complex variables with a manifold of connections to quantum mechanics, signal analysis, probability, planar orthogonal polynomials, statistical spectral estimation, geometry of three-dimensional surfaces, and number theory. For such spaces, explicit large sieve constant estimates are obtained. A number of extensions of the result to other settings (with the hyperbolic geometry associated with wavelets, with the disc or spherical geometries, or to deBranges spaces, for instance) is suggested, as well as some open problems. A further question raised by this work is the investigation of the proper planar analogue of Beurling extremal theory, which we were unable to find in the literature. |
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Carlos BraumannUniversidade de ÉvoraMathematical Biology: Stochastic Differential Equations Modelling Examples
The dynamics of some biological phenomena are frequently modelled using ordinary differential equations (ODE). However, quite often random environmental fluctuations do affect the dynamics of these phenomena in a significant way and, besides causing considerable deviations from the mean dynamics, may also produce new qualitative features. Incorporating the effect of random environmental fluctuation leads to stochastic differential equation (SDE) models.
The other advantage of using SDE models is that the statistical issues of estimation, model choice, prediction (and its degree of precision) and hypothesis testing become quite natural (so to speak, built in the model). Contrary to ODE models, one does not need to artificially impose these issues as an outer layer (like a regression structure). Regression methods are quite convenient to deal with measurement errors of deterministic dynamics, but are totally inadequate to deal with true randomness affecting the very dynamics.
We will present a few applications of SDE models in Mathematical Biology, based on some recent and some not so recent publications of the author and the co-authors Patrícia A. Filipe, Clara Carlos and Nuno M. Brites. Namely, we will address: a) Models for the growth of animal populations, including the qualitative behaviour of general models (in what concerns extinction and existence of a stationary density) and the effect of using approximate models. b) Harvesting models and profit optimization using variable and constant fishing efforts. c) Models for individual growth of an animal and extension to mixed models for several animals, with applications to profit optimization of bovine growers. A brief reference will be made to the stochastic calculi of Itô and Stratonovich and its incidence on modelling. |
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Emilio CarizosaUniversidad de SevillaMathematical Optimization (or not) in Data Science
Many challenges in Data Science are reduced in one way or another to a mathematical optimization problem, usually nonconvex and involving both continuous and integer variables. Hence, traditional procedures searching zero gradient solutions are not applicable, and alternative, computer-intensive algorithms, are required.
In this talk we will review some data analysis problems and the mathematical optimization tools used to address them.
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Joan MateuUniversitat Autònoma de BarcelonaEuler Equation and Dislocations
In this talk I will present some results obtained in the last years on the existence of planar rotating vortex patches for the 2-D Euler equation, and how this problem is related with a question on the properties of materials: the dislocations. More precisely, I will present a characterization of the minimizers for a given nonlocal energy.
These minimizers coincide with the family of Kirchhoff ellipses which are rotating vortex patches for the 2-D Euler equation.
I will show how some techniques in harmonic analysis, singular integral and fractional integrals, are useful to solve this kind of problems.
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Joan SaldañaUniversitat de GironaHuman Behaviour in Epidemic Modelling
Preventive behaviours in response to the presence of an infec- tious disease have a strong impact on the spread of the disease itself. Risk perception triggers reactions as, for instance, social distancing or wearing face masks, which are aimed to reduce contagion risk. In turn, these preventive behaviours have an effect on the course of an epidemic by reducing the transmission of a communicable disease in different ways (e.g., diminishing/changing social contacts or reducing the probability of passing the infectious agent during a physical contact). In this talk, we will present different approaches that have been recently developed to capture individual behavioural responses in epidemic models in order to measure their impact on disease transmissibility.
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João XavierIST, Universidade de LisboaDistributed Learning Algorithms for Big Data
Modern datasets are increasingly collected by teams of agents that are spatially distributed: sensor networks, networks of cameras, and teams of robots. To extract information in a scalable manner from those distributed datasets, we need distributed learning. In the vision of distributed learning, no central node exists; the spatially distributed agents are linked by a sparse communication network and exchange short messages between themselves to directly solve the learning problem.
To work in the real-world, a distributed learning algorithm must cope with several challenges, e.g., correlated data, failures in the communication network, and minimal knowledge of the network topology.
In this talk, we present some recent distributed learning algorithms that can cope with such challenges. Although our algorithms are simple extensions of known ones, these extensions require new mathematical proofs that elicit interesting applications of probability theory tools, namely, ergodic theory.
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| Organizers | Diogo Oliveira e Silva (University of Birmingham) Gustavo Garrigós (Universidad de Murcia) |
| Organizers | João Gama (Universidade do Porto) Pedro Delicado (Universitat Politècnica de Catalunya) |
| Organizers | Raquel Barreira (Instituto Politécnico de Setúbal) Silvia Cuadrado (Universitat Autònoma de Barcelona) |
