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Obstructions for submanifolds in low codimension

Speacker: Christos-raent Onti - IMPA
Tue 29 May 2018, 15:30 - Sala 236Differential Geometry

Abstract: By the Nash’s embedding theorem, every Riemannian manifold can be isometrically immersed into a Euclidean space with sufficiently high codimension. However, there are results that impose restrictions on isometric immersions with low codimension. In our talk, we will present integral curvature bounds in terms of the Betti numbers for compact submanifolds of the Euclidean space with low codimension. Applications will also be given. This is a joint work with Th. Vlachos.


Marcinkiewicz inequalities in de Branges spaces

Speacker: Friedrich Littmann - North Dakota State University - USA
Tue 29 May 2018, 15:30 - Sala 232Analysis and Partial Differential Equations

Abstract: The classical Marcinkiewicz inequality compares discrete and integral $p$-norms in polynomial spaces. In 2000, Mastroianni and Russo considered weighted versions of this inequality, and they found a substantial generalization in the case when the weight is a doubling measure. This talk discusses the adjustments that are necessary to prove analogous weighted inequalities in spaces of entire functions of exponential type if the underlying measure comes from a de Branges space.


Alguns Problemas de Controle de Doenças Vetoriais: Modelagem e Análise

Speacker: Maria Soledad Aronna - FGV/EMAp - Escola de Matemática Aplicada
Tue 29 May 2018, 17:00 - Sala 232Special Talk

Abstract:

Nesta palestra vou apresentar dois trabalhos que tratam sobre a redução da transmissão de doenças vetoriais através do controle do vetor (que seria o mosquito nos casos aqui estudados). No primeiro trabalho modelamos o processo de introdução da bactéria Wolbachia numa população de Aedes aegypti. A Wolbachia é uma bactéria intracelular maternalmente transmitida, e quando está presente no Aedes aegypti consegue limitar a capacidade do mosquito de transmitir a dengue, zika e chikungunya. O modelo sugerido é constituído por um sistema de EDOs não-lineares controladas. Para este modelo estudamos a obtenção de uma lei em forma de “feedback” que permite levar o sistema ao equilíbrio de infestação total. O segundo trabalho trata da presença da malária na região amazônica. É sabido que nessa área a piscicultura contribui na transmissão da doença, dado que a atividade é realizada em tanques artificiais que têm se transformado em espaços atrativos para os mosquitos depositarem seus ovos. Foi observado que a limpeza da vegetação dos bordos dos tanques de cultivo ajuda a controlar o tamanho da população de mosquitos. Nesse trabalho apresentamos um modelo que representa a relação entre os tanques, a população de mosquitos e a transmissão da malária. Utilizamos esse modelo para quantificar a contribuição efetiva dos tanques na epidemia. O modelo é constituído por um sistema de EDOs não-lineares com saltos nos instantes de limpeza, que agem como “controles impulsivos”. Estudamos o comportamento assintótico do sistema em função da intensidade e periodicidade da limpeza.


From the Geometry of Extreme Value Distributions to Improved Tail Fitting in Market Data

Speacker: William F. Shadwick - Omega Analysis
Mon 04 Jun 2018, 17:00 - Sala 232Mathematical Methods in Finance

Abstract: A new geometric invariant explains and unifies the landmark results of Extreme Value Theory. This invariant also provides an intrinsic measure of the rate of convergence of tails of probability distributions to their Extreme Value limits.

Tail models that converge rapidly over quantile ranges that are practical in financial applications are highly efficient.

Some recent applications include ‘flash crashes’, multi-day drawdown risk in bank share prices and in Short VIX positions and early warning signals of asset price bubbles as well as a measure of their severity.


Harmonic energy and geometric non-formality

Speacker: Dmitri Scheglov - UFMG
Tue 05 Jun 2018, 15:30 - Sala 236Differential Geometry

Abstract: For compact oriented 2n-dimensional manifolds we introduce a "geometric formality" functional on the space of Riemannian metrics which measures the failure of the product of two harmonic n-forms to be harmonic.For the "first nontrivial case", which is a genus two surface, we were able to completely describe the (essentially) finite-dimensional minimal locus of this functional in the space of all riemannian metrics. All the metrics in the minimal locus have interesting property that their curvature is non-positive and is zero exactly at Weierstrass points.


Forecasting Large Realized Covariance Matrices: The Benefits of Factor Models and Shrinkage

Speacker: Marcelo Cunha Medeiros - PUC-RJ
Tue 05 Jun 2018, 17:30 - Sala 232Mathematical Methods in Finance

Abstract: We propose a model to forecast very large realized covariance matrices of returns, applying it to the constituents of the S\&P 500 on a daily basis. To address the curse of dimensionality, we decompose the return covariance matrix using standard firm-level factors (e.g., size, valueand profitability) and use sectoral restrictions in the residual covariance matrix. This restricted model is then estimated using vector heterogeneous autoregressive (VHAR) models estimated with theleast absolute shrinkage and selection operator (LASSO). Our methodology improves forecasting precision relative to standard benchmarks and leads to better estimates of the minimum variance portfolios.


Ratcheting pairs of droplets

Speacker: Carlos Galeano-ríos - Math. Dept., University of Bath, Inglaterra
Wed 06 Jun 2018, 11:00 - Sala 333Applied and Computational Mathematics

Abstract: Within a certain parameter regime, millimetric droplets can be made to bounce indefinitely on the free surface of a vertically vibrating bath. When two of these bouncing droplets are placed close to each other they interact through the surface wavefield. When the droplets are of different sizes, they spontaneusly start moving along the line of their centres in a ratchet-like fashion, while keeping a roughly constant separation distance. As the shaking amplitude of the bath changes, the droplet pairs reverse their direction of motion up to three times. In this work we combine experimental explorations with detailed modelling to uncover the underlying mechanisms that yield this ratcheting behaviour. We highlight the importance of the propagating fronts that are triggered at each impact and their role in setting the separation distances.


Mineração de dados com documentos históricos: uma abordagem sobre modelagem de tópicos e processamento de linguagem natural

Speacker: Marcelo Ribeiro - FGV
Wed 13 Jun 2018, 13:30 - Auditorio 3Computer Graphics

Abstract:

O objetivo desta palestra é apresentar resultados obtidos com a aplicação de modelos e técnicas de mineração de dados textuais ligados às áreas de Machine Learning e Processamento de Linguagem Natural. A base de dados utilizada faz parte do acervo do CPDOC-FGV e compreende essencialmente documentos históricos da década de 1970 pertencentes a Antonio Azeredo da Silveira, ex-ministro de Relações Exteriores do Brasil. Além da abordagem sobre os métodos aplicados, haverá menção às etapas de pré-processamento, que foram essenciais para que o projeto atingisse resultados satisfatórios.


Fibrewise bundles over the Gromov-Hausdorff space

Speacker: C. A. Morales - UFRJ/Chungnam National University, Daejeon, South Korea.
Tue 14 Aug 2018, 13:30 - Sala 232Dynamical Systems

Abstract: The Gromov-Hausdorff space is the set Mof compact metric spaces up to isometries, equippedwith the Gromov-Hausdorff metric.In this lecture we will studyAct(G), the spaceofG-actions over compact metric spacesup to isometric conjugacy. We present a metricinAct(G)extending [Arbieto-Morales, DCDS2017] yieldinga fibrewise space structure overM.Some properties of Act(G)asfibrewise space over Mwill be discused.