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07/05/2014, 15:00 — 16:00 — Room P3.10, Mathematics Building

Hildebrando Rodrigues, *Universidade de São Paulo (São Carlos)*

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Synchronization and Applications

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23/04/2014, 15:00 — 16:00 — Room P3.10, Mathematics Building

Diogo Oliveira e Silva, *Hausdorff Center for Mathematics da Universidade de Bona*

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On extremizers for Fourier restriction inequalities

This talk will focus on extremizers for a family of Fourier
restriction inequalities on planar curves. It turns out that,
depending on whether or not a certain geometric condition related
to the curvature is satisfied, extremizing sequences of nonnegative
functions may or may not have a subsequence which converges to an
extremizer. We hope to describe the method of proof, which is of
concentration compactness flavor, in some detail. Tools include
bilinear estimates, a variational calculation, a modification of
the usual method of stationary phase and several explicit
computations.

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08/04/2014, 14:00 — 15:00 — Abreu Faro Amphitheatre

Lloyd Demetrius, *Harvard University and Max Planck Institute of Molecular Biology, Berlin*

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An entropic selection principle of evolutionary theory

The outcome of competition between populations of replicating
entities is predicted by evolutionary entropy, a nonequilibrium
analogue of the Gibbs-Boltzmann entropy in statistical
thermodynamics. This talk will outline the mathematical basis of
this selection principle and describe certain applications to the
origin of metabolic diseases.

#### See also

http://www.sciencedirect.com/science/article/pii/S0370157313001191#

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04/06/2013, 15:00 — 16:00 — Room P3.10, Mathematics Building

Christian Le Merdy, *Université de Franche-Comté*

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Dilation of operators on $L^p$-spaces

Let $1\lt p \lt\infty$, let $(\Omega,\mu)$ be a measure space and let $T : L^p(\Omega)\to L^p(\Omega)$ be a bounded operator. We say that it admits a dilation (in a loose sense) when there exist another measure space $(\Omega',\mu')$, an invertible operator $U$ on ${L^p}(\Omega')$ such that $\{U^n:n\in\mathbb{Z} \}$ is bounded and two bounded operators $J : L^p(\Omega) \to L^p(\Omega')$ and $Q : L^p(\Omega')\to L^p(\Omega)$ such that $T^n=Q {U^n} J$ for any integer $n\ge 0$. When $p=2$, this property is equivalent to $T$ being similar to a contraction. The main question considered in this talk is to characterize operators with this property when $p\ne 2$. Our results give partial answers and strong connections with functional calculus properties. The talk will include motivation for this dilation question. (Joint work with C. Arhancet.)

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14/05/2013, 15:00 — 16:00 — Room P3.10, Mathematics Building

Filippo Cagnetti, *University of Sussex*

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A new method for large time behavior of convex Hamilton-Jacobi
equations

We introduce a new method to study the large time behavior for
general classes of Hamilton-Jacobi type equations, which include
degenerate parabolic equations and weakly coupled systems. We
establish the convergence results by using the nonlinear adjoint
method and identifying new long time averaging effects. These
methods are robust and can easily be adapted to study the large
time behavior of related problems.

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16/04/2013, 15:00 — 16:00 — Room P3.10, Mathematics Building

Florin Radulescu, *Università di Roma - Tor Vergata*

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Ramanujan-Petersson conjectures and Operator Algebras

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02/04/2013, 15:00 — 16:00 — Room P3.10, Mathematics Building

Jorge Ferreira, *Universidade Federal Rural de Pernambuco*

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On the asymptotic behaviour of nonlocal nonlinear problems

This lecture deals with nonlocal nonlinear problems. Our main results concern existence, uniqueness and asymptotic behavior of the weak solutions of a nonlinear parabolic equation of reaction-diffusion nonlocal type by an application of the Faedo-Galerkin approximation and Aubin-Lions compactness result. Moreover, we prove continuity with respect to the initial values, the joint continuity of the solution and a result on the existence of the global attractor for the problem \[ \begin{cases} u_{t}-a(l(u))\Delta u+| u|^{\rho }u=f(u) \phantom{.} \text{ in} \phantom{.} \Omega \times (0,T), \\ u(x,t)=0 \phantom{.} \text{ on }\phantom{.} \partial \Omega \times (0,T), \\ u(x,0)=u_{0}(x) \phantom{.}\text{ in }\phantom{.} \Omega , \end{cases} \] when $0\lt \rho \le 2/(n-2)$ if $n\ge 3$ and $0\lt \rho \lt \infty $ if $n=1,2$, where $u=u(x,t)$ is a real valued function, $\Omega \subset \mathbb{R}^{n}$ is a bounded smooth domain, $n\ge 1$ with regular boundary $\Gamma =\partial \Omega $, $p\geq 2$. Moreover, $a$ and $f$ are continuous functions satisfying some appropriate conditions and $l: L^{2}(\Omega )\to\mathbb{R}$ is a continuous linear form.

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14/12/2012, 11:00 — 12:00 — Room P3.10, Mathematics Building

Rafael de la Llave, *Georgia Tech.*

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Manifolds on the verge of a regularity breakdown

There are two main stabibility arguments for solutions in dynamical
systems: the theory of normal hyperbolicity and the Kolmogorov
Arnold Moser theory of perturbations. In recent times, there has
been progress in developing versions of the theory that are well
suited for computations. The theory does not require that the
system is close to integrable, but rather uses geometric
identities. The theorems prove that approximate solutions
satisfying some non-degeneracy assumptions correspond to a true
solution. Furthermore, the proofs lead at the same time to very
efficient algorithms. Implementing these algorithms, leads to some
conjectural insights on the phenomena that happen at breakdown.
They turn out to be remarkably similar to phenomena that were
observed in phase transition and "renormalization group" provides a
unifying point of view. Nevertheless, many questions remain open.

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27/11/2012, 15:00 — 16:00 — Room P3.10, Mathematics Building

Jinjun Li, *Instituto Superior Técnico*

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Topological entropy of refined irregular sets

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16/07/2012, 15:00 — 16:00 — Room P3.10, Mathematics Building

David Owen, *Carnegie Mellon University*

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Multiscale Geometrical Changes in Continua: Structured Deformations
and Some Questions in Analysis

Classes of injective deformations of a continuous body that are
stable under composition and under the taking inverses are central
to the description of geometrical changes of a continuous body at
both the macroscopic and microscopic levels. Classical, simple, and
structured deformations are described and assessed from the point
of view of continuum mechanics and of variational problems. The
natural way of assigning an energy to a structured deformation,
through relaxation of an energy assigned to a smaller class of
deformations, leads to various alternative, "variationally
friendly" notions of structured deformations. Several of these
alternative notions are examined from the point of view of
approximation by deformations in a smaller class and of relaxation
of an initial energy defined on the smaller class of deformations.
Questions are raised as to whether or not different notions of
structured deformations lead to different relaxed energies for a
structured deformation that satisfies the defining requirements of
two or more notions. A recent example of an explicit formula for a
relaxed energy is used to illustrate these questions.

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10/07/2012, 15:00 — 16:00 — Room P3.10, Mathematics Building

Roman Hric, *Matej Bel University, Banska Bystrica, Slovakia*

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Dense orbits of homeomorphisms, flows and their time maps

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24/04/2012, 15:00 — 16:00 — Room P3.10, Mathematics Building

Henrique Oliveira, *Instituto Superior Técnico*

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New Results on the Collatz Problem

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03/04/2012, 14:00 — 15:00 — Room P3.10, Mathematics Building

Saber Elaydi, *Trinity University, San Antonio, USA*

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Application of singularity theory in planar discrete dynamical
systems and applications to competition models

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13/03/2012, 15:00 — 16:00 — Room P3.10, Mathematics Building

George Sell, *University of Minnesota*

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How to use numerical techniques to study the dynamics inside the
attractor

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16/02/2012, 15:00 — 16:00 — Room P3.10, Mathematics Building

José Ferreira Alves, *Universidade do Porto*

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Gibbs-Markov structures vs statistical properties in dynamical
systems

In a classical approach to dynamical systems one frequently uses
certain geometric structures of the system to deduce statistical
properties, such as invariant measures with stochastic-like
behaviour, large deviations or decay of correlations. Such
geometric structures are generally highly non-trivial and thus a
natural question is the extent to which this approach can be
applied. We show that in many cases stochastic-like behaviour
itself implies that the system has certain geometric properties,
which are therefore necessary as well as sufficient conditions for
the occurrence of the statistical properties under consideration.

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18/10/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building

Bernold Fiedler, *Freie Universität Berlin*

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Schoenflies spheres in Sturm attractors

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22/06/2011, 16:00 — 17:00 — Room P3.10, Mathematics Building

Diogo Oliveira e Silva, *University of California, Berkeley*

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On trilinear oscillatory integrals

We examine a certain class of trilinear integral operators which incorporate oscillatory factors ${e}^{iP}$, where $P$ is a real-valued polynomial, and prove smallness of such integrals in the presence of rapid oscillations. Tools include sublevel set estimates, higher dimensional versions of van der Corput's lemma and corresponding multilinear analogues. This is joint work with Michael Christ.

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24/05/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building

Felipe Rivero, *Universidad de Sevilla*

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Structure stability of pullback attractors

Attractors help us to understand the dynamics of a system thanks to the asymptotic information given about the solutions. But any mathematical object needs a robust definition, that is, needs consistence under perturbations, because any physical model might experiment any kind of natural or artificial changes. Our aim in this talk is to show how a gradient-like pullback attractor has a stable structure under small perturbations and show some nontrivial examples where the perturbation can be found in the time dependent operator or in the nonlinearity.

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15/03/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building

Bernold Fiedler, *Institute of Mathematics, Free University of Berlin*

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Negative Bendixson-Dulac criteria in several dimensions? A chemostat example

The negative criterium of Bendixson and Dulac states that area contracting planar vector fields cannot possess periodic orbits. A physics student asked in class why this would not generalize to three dimensions, obviously, using the curl. We give a higher-dimensional example, arising from chemostats, where a suitable differential form excludes periodicity. This is joint work with Sze-Bi Hsu.

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07/12/2010, 15:00 — 16:00 — Room P3.10, Mathematics Building

Manuel de León, *ICMAT-Consejo Superior de Investigaciones Cientificas*

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Generalized Hamiltonian systems and applications to nonholonomic
mechanics

Over twenty years ago Alan Weinstein proposed to formulate
mechanics in the framework of Lie algebroids. The use of Lie
algebroids in mechanics has recently permitted two unexpected
applications: the development of a Hamilton--Jacobi theory and a
simple reduced scheme for nonholonomic mechanical systems.