Encontros IST-IME 

09/09/2022, 15:45 — 16:30 — Anfiteatro Abreu Faro
Luís Barreira, Instituto Superior Técnico, Universidade de Lisboa

Spectra of delay equations

09/09/2022, 15:00 — 15:45 — Anfiteatro Abreu Faro
Carlos Rocha, Instituto Superior Técnico, Universidade de Lisboa

Order Preserving Semiflows Revisited

Dynamical systems generated by scalar reaction-diffusion equations enjoy special properties that lead to a very simple structure for the semiflow. Among these properties, the monotone behavior of the number of zeros of the solutions plays an essential role. This discrete Lyapunov functional, the zero number, contains important information on the spectral behavior of the linearization and leads to the simple description of the dynamical system.

Other systems possess this kind of discrete Lyapunov functional and we review some classes of linear equations that generate semiflows with this property. Moreover, we ask if this property is characteristic of such problems.

This is based on a joint work with Giorgio Fusco.

Ver também

ISTIME2022 CRocha.pdf

09/09/2022, 12:15 — 13:00 — Anfiteatro Abreu Faro
Jorge Drumond Silva, Instituto Superior Técnico, Universidade de Lisboa

Nonlinear smoothing by the infinite normal form reduction method.

09/09/2022, 11:30 — 12:15 — Anfiteatro Abreu Faro
Jaime Angulo Pava, Universidade de São Paulo

The NLS equation on tadpole graphs and beyond

09/09/2022, 09:45 — 10:30 — Anfiteatro Abreu Faro
Pedro Duarte, Faculdade de Ciências, Universidade de Lisboa

Stability of the Lyapunov exponents of randomly perturbed quasi-periodic cocycles

The study of linear cocycles and their Lyapunov exponents in Ergodic Theory has an important interface with study of spectral properties of discrete Schrödinger operators in Mathematical Physics, namely via the regularity of the Lyapunov exponents of the Schrödinger cocycles which relate to the spectral properties of the associated Schrödinger operators. Many results have been obtained so far on the continuity of the Lyapunov exponents for two main classes of linear cocycles: the class of quasi-periodic linear cocycles and the class of random linear cocycles. In this talk, I will survey on recent work with Ao Cai and Silvius Klein on a problem posed by Jiangong You about the stability of the Lyapunov exponents for random perturbations of quasi-periodic Schrödinger cocycles.

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PedroDuarteISTIME22.pdf

09/09/2022, 09:00 — 09:45 — Anfiteatro Abreu Faro
Marcelo Viana, Instituto de Matemática Pura e Aplicada

Thermodynamic u-formalism

08/09/2022, 15:45 — 16:30 — Anfiteatro Abreu Faro
Diogo Gomes, KAUST

Monotone operator techniques in mean-field games

08/09/2022, 15:00 — 15:45 — Anfiteatro Abreu Faro
Radoslaw Czaja, University of Silesia in Katowice

Finite-dimensional attractors for dissipative fourth order problems in $\mathbb{R}^{N}$

08/09/2022, 12:15 — 13:00 — Anfiteatro Abreu Faro
José Matias, Instituto Superior Técnico, Universidade de Lisboa

Upscaling and spatial localization of non-local energies with applications to crystal plasticity

An integral representation result is obtained for the asymptotics of energies including both local and non-local terms, in the context of structured deformations.

Starting from an initial energy featuring a local bulk and interfacial contribution and a non-local measure of the jump discontinuities, an iterated limiting procedure is performed. First, the initial energy is relaxed to structured deformation, and then the measure of non-locality is sent to zero, with the effect of obtaining an explicit local energy in which the non-linear contribution of submacroscopic slips and separations is accounted for. Two terms, different in nature, emerge in the bulk part of the final energy: one coming from the initial bulk energy and one arising from the non-local contribution to the initial energy. This structure turns out to be particularly useful for studying mechanical phenomena such as yielding and hysteresis. Moreover, in the class of invertible structured deformations, applications to crystal plasticity are presented.

This is a joint work with Marco Morandotti, David R. Owen, and Elvira Zappale.

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ISTIME Matias.pdf

08/09/2022, 11:30 — 12:15 — Anfiteatro Abreu Faro
Fernando Pestana da Costa, Universidade Aberta

A coagulation type model for silicosis

We introduce an infinite dimensional system of ordinary differential equations modelling silicosis, and discuss results on existence, uniqueness, basic properties of solutions, and, for a family of coefficients, the structure of equilibria and their linear stability properties, which allow us to understand the local bifurcation of equilibria.

The reported results are based on joint works with P. Antunes, M. Drmota, M. Grinfeld, J. Pinto and R. Sasportes.

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FPC_Lisboa2022_talk.pdf

08/09/2022, 10:30 — 11:15 — Anfiteatro Abreu Faro
José Arrieta, Universidad Complutense de Madrid

Boundedness of solutions of nonautonomous logistic equations

08/09/2022, 09:45 — 10:30 — Anfiteatro Abreu Faro
Alexandre Carvalho, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos

Inertial Manifolds, Saddle Point Property and Exponential Dichotomy: A unified theory

Inertial manifold theory, saddle point property and exponential dichotomy have been treated as different topics in the literature with different proofs.

As a common feature, they all have the purpose of ‘splitting’ the space to understand the dynamics. We present a unified proof for the inertial manifold theorem, which as a local consequence yields the saddle-point property with a fine structure of invariant manifolds and the roughness of exponential dichotomy.

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Alexandre_Carvalho_ISTIME_2022.pdf

08/09/2022, 09:00 — 09:45 — Anfiteatro Abreu Faro
Clodoaldo Grotta Ragazzo, Universidade de São Paulo

Vortices on surfaces: a history in motion.

07/09/2022, 12:15 — 13:00 — Anfiteatro Abreu Faro
Ronaldo Garcia, Universidade Federal de Goiás

The mathematical work of Jorge Sotomayor: bifurcation theory and qualitative theory of principal lines.

The goal of this talk is to present, in a historical perspective, the contributions of Jorge Sotomayor (25/03/1942-07/01/2022) in two areas. Namely, his work in bifurcations of codimension one, two and three of vector fields, and the qualitative theory of principal lines on surfaces and hypersurfaces.

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Palestra_8th_ISTIME_ronaldo.pdf

07/09/2022, 11:30 — 12:15 — Anfiteatro Abreu Faro
Gustavo Granja, Instituto Superior Técnico, Universidade de Lisboa

Topology of almost complex structures in dimension $6$

07/09/2022, 09:45 — 10:30 — Anfiteatro Abreu Faro
Diogo Oliveira e Silva, Instituto Superior Técnico, Universidade de Lisboa

Sharp restriction theory: highlights and future directions

07/09/2022, 09:00 — 09:45 — Anfiteatro Abreu Faro
Edson de Faria, Universidade de São Paulo

Rigidity and orbit-flexibility of circle maps

06/09/2022, 15:45 — 16:30 — Anfiteatro Abreu Faro
Miguel Abreu, Instituto Superior Técnico, Universidade de Lisboa

Periodic orbits of Reeb flows and the Ehrhart polynomial of toric diagrams

06/09/2022, 15:00 — 15:45 — Anfiteatro Abreu Faro
Gláucio Terra, Universidade de São Paulo

The Smoothing Problem in Chow-Rashevskii

06/09/2022, 12:15 — 13:00 — Anfiteatro Abreu Faro
Simão Correia, Instituto Superior Técnico, Universidade de Lisboa

Stable perturbations of self-similar solutions for the modified KdV at the blow-up time