Palestrantes confirmados:
Differential models to capture different behaviors of glioblastoma.
Data: 04/01
Hora: 16h
Palestrante: Francisco Guillen-Gonzalez - Universidade de Sevilha
Resumo: Glioblastoma (GBM) is a highly proliferative brain tumor. According to quantitative studies [1,2], using a large number of magnetic resonances of GBMs, different behaviors appear according to two criteria:
1. The width of the ring that forms proliferating cells around necrotic cells, [1].
2. Regular or irregular growth of the GBM surface, [2].
From an experimental point of view, there is a correlation between these different behaviors and the average life expectancy of the tumor [1,2], .
In this talk we are going to describe a general model of interaction between 3 variables (proliferating and necrotic cells, with the vasculature) by means of a hybrid differential system (1 partial differential equation for proliferating cells and 2 ordinary differential equations for necrotic cells and for vasculature), which can capture the different behaviors described above by changing the values of parameters. After describing the mathematical modeling part, some theoretical and numerical results will be enunciated for two particular problems (one with non-linear diffusion and the other one with a chemotaxis term). Finally, some numerical simulations will be show veryfing the different behaviors.
All these results are part of a joint work with A. Fernández-Romero and A. Suárez (University of Seville), which have finalized in AFR’s PhD thesis, [3,4,5,6].
Para ver o documento acesse.
Keywords: Glioblastoma, hybrid differential systems, nonlinear diffusion, chemotaxis.
Waring problems and the Lefschetz properties
Data: 06/01
Hora: 16h
Palestrante: Rodrigo Gondim - UFRPE
Resumo: We study three variations of the Waring problem for homogeneous polynomials. The Waring problem comes from number thery. It asks, for a fixed exponent, the minimal number of summands such any whole number can be written as a sum of powers. We will be interested in the Waring rank, the border rank and the cactus rank of a form. We show how the Lefschetz properties of the associated algebra affect them. We construct new families of wild forms, that is, forms whose cactus rank, of schematic nature, is bigger than the border rank, defined geometrically. (Joint with T. Dias, UFRPE)
Complexidade Computacional de Problemas em Grafos
Data: 13/01
Hora: 16h
Palestrante: Ana Shirley Silva - Universidade Federal do Ceará.
Resumo: O que significa dizer que um problema é difícil? Nesta palestra, irei apresentar as definições básicas de Teoria da Complexidade Computacional que levam ao Problema do Milênio P vs. NP. Além disso, apresentarei conceitos mais modernos de complexidade computacional (Complexidade Parametrizada) e darei algumas noções de Teoria dos Grafos, abordando alguns dos problemas que tenho estudado mais recentemente.
On a weakly coupled nonlinear Choquard system with logarithm kernel
Data: 20/01
Hora: 16h
Palestrante: Jonison Lucas dos Santos Carvalho - Universidade Federal de Sergipe.
Resumo: In this talk we discuss the existence of solutions for a class of coupled nonlinear logarithmic Choquard equations. We analyze when the system admits semi-trivial solution or vector solution. Our approach is based on minimization over Nehari manifold and a version of the Principle of Symmetric Criticality due to Palais.
Joint work with J. C. de Albuquerque (Federal University of Pernambuco) and E. Medeiros (Federal University of Paraíba).
Soliton solutions to the curve shortening flow on the 2-dimensional hyperbolic space.
Data: 27/01
Hora: 16h
Palestrante: Keti Tenenblat - UnB.
Resumo: We prove that a curve is a soliton solution to the curve shortening flow on the 2-dimensional hyperbolic space if and only if its geodesic curvature is given as the inner product between its tangent vector field and a vector of the 3-dimensional Minkowski space. We prove that there are three classes of such solutions and for each fixed vector there exits a 2-parameter family of soliton solution to the curve shortening flow on the 2-dimensional hyperbolic space. Moreover, we prove that each soliton is defined on the whole real line, it is embedded and its geodesic curvature, at each end, converges to a constant.
This is a joint work with Fabio Nunes da Silva (Universidade Federal do Oeste da Bahia).
Mating quadratic maps with the modular group
Data: 04/02
Hora: 16h
Palestrante: Luna Lomonaco - IMPA.
Resumo: Holomorphic correspondences are polynomial relations P(z,w)=0, which can be regarded as multi-valued self-maps of the Riemann sphere, this is implicit maps sending z to w. The iteration of such a multi-valued map generates a dynamical system on the Riemann sphere: dynamical system which generalises rational maps and finitely generated Kleinian groups. We consider a specific 1-(complex)parameter family of (2:2) correspondences F_a (introduced by S. Bullett and C. Penrose in 1994), which we describe dynamically. In particular, we show that for every parameter in a subset of the parameter plane called 'the connectedness locus' and denoted by M_{\Gamma}, this family behaves as rational maps on a subset of the Riemann sphere and as the modular group on the complement: in other words, these correspondences are mating between the modular group and rational maps (in the family Per_1(1)). Moreover, we develop for this family of correspondences a complete dynamical theory which parallels the Douady-Hubbard theory of quadratic polynomials, and we show that M_{\Gamma} is homeomorphic to the parabolic Mandelbrot set M_1. This is joint work with S. Bullett (QMUL).
Blow-up and global solutions for semilinear parabolic equations
Data: 10/02
Hora: 16h
Palestrante: Juliana Fernandes Pimentel - Universidade Federal do Rio de Janeiro.
Resumo: We apply comparison principle and variational methods to a class of semilinear parabolic equations. The ultimate goal is to analyze the behavior of the solutions as the initial data varies in the phase space. In particular, the Nehari manifold is used to separate the phase space into regions of initial data where uniform boundedness or blow-up behavior of the semiflow may occur.
Trudinger–Moser-type inequality in weighted spaces
Data: 18/02
Hora: 16h
Palestrante: Joao Marcos Bezerra do O - Universidade Federal da Paraíba.
Resumo: We establish a Trudinger-Moser-type inequality in weighted Sobolev spaces. Moreover, working in weighted Sobolev spaces, we prove the existence of a bound state solution for a class of Schrödinger equations with critical exponential growth. Our approach is based on a weighted Trudinger-Moser-type inequality and the classical mountain pass theorem.
Um survey sobre reprodutividade e periodicidade no tempo para fluidos incompressíveis
Data: 22/02
Hora: 16h
Palestrante: Marko Antonio Rojas Medar - Universidad de Tarapacá.
Resumo: Nesta palestra, o objetivo é revisar alguns resultados que estão atualmente disponíveis na literatura sobre existência, unicidade e regularidade de soluções reprodutivas e periódicas no tempo para as equações de Navier-Stokes e algumas variantes. Ademais, apresentaremos alguns problemas em aberto.
A TOUR ON LEFSCHETZ PROPERTIES
Data: 24/02
Hora: 16h
Palestrante: Aline Andrade.
Resumo: Inspired by the Hard Lefschetz Theorem from algebraic topology, we say that an artinian graded algebra is said to possess weak Lefschetz property if the multiplication by a general linear form has maximal rank at every degree. There is a huge amount of work done trying to study these properties, whether trying to classify algebras that have them or trying to find algebras that do not. Surprisingly these studies led to the discovery of connections of the Lefschetz properties, with other areas of mathematics, for instance, with differential and algebraic geometry, combinatorics and representation theory.
In this expository talk, we are going to define the basic definitions needed to study the Lefschetz Properties, then we will present some connections with algebraic geometry, and discuss some open problems.