ICM opens the science to the society within the Congress of the Future

On the occasion of the Congress of the Future, an space for exchange of ideas between Chileans and world class thought leaders, Millennium Science Initiative organizes two activities, which are free and open to the public, in Valparaíso (Chile). The first one, which will take place on 22th January  2016.  It will be a conference in cooperation with the German Max-Planck Societ. The purpose is to deepen the collaboration and to spread the work of these centers to the rest of the scientific community.  The other two events are an opening table on “Science and Development” and a Plenary Conference carried out by PhD  Peter Seeberger, Director at the Max-Planck Institute for Colloids and Interfaces.

CAPDE brings closer Japanese-Chilean research in PDEs

The third  workshop Chile-Japon on Nonlinear PDEs, which was partly supported by CAPDE along with Japan funding, took place in Osaka University from 8 to 11 December 2015.

It was aimed to bring together experts in the field of nonlinear partial differential equations from Chile and Japan. The meeting was intented to present recent advances in the area, whose problems play a key role in modeling biological pattern formation, mathematical ecology, material science and superconductivity, among other fields.

“It is very important for the Chilean and Japanese groups the interaction, to know what the others are doing, as well as to strengthen the possibility of postdoctoral exchanges”, pointed out Manuel del Pino, main researcher of Capde.

Topics covered included semilinear parabolic system, singular perturbation problems or competitive system of chemotaxis. The event was attended by 60 people and 22 speakers, 11 of them from Chie.

So, Del Pino, in his abstract “Bubbling in the critical heat equation: the role of Green’s function”, explained the point-wise, infinite-time bubbling phenomenon for positive solutions of the semilinear heat equation at the critical exponent in a bounded domain. On the other side, Claudio Muñoz´s abstracts was entitled “Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NovikovVeselov equation”. Alexander Quaass talked about large solutions for some local and non-local nonlinear elliptic equations Break and Mónica Musso foucused on a non-compactness result on the fractional Yamabe problem in large dimensions. Also Ignacio Guerra shared his investigation, on“Multiplicity of solutions for an elliptic equation with a singular nonlinearity and a gradient term”.

Participants agreed to celebrate the fourth edition of this workshop in 2017 in Universidad Federico Santa María (USM). The first workshop was held in 2007 at the Center for Mathematical Modeling (CMM) of Universidad de Chile and the second in 2010 in Tokyo.

For more information, see the website of the 3rd Chile-Japan Worshop on Nonlinear EDPs.

CAPDE invites you to a poetic walk through mathematics

“Nice Concepts- a poetic walk through mathematics” , the educational video supported by Capde and produced by  the Department of Mathematical Engineering of Universidad de Chile, is already available on youtube.  It explains different mathemtical notions, for instance, Brachistochrone curve or Geodesic.  These concepts are presented by professors of the Departament. Two of them are Manuel del Pino and Claudio Muñoz, CAPDE´s researchers too. They talked about the heat equation, which studies how temperature vary deppending how far or how close the energy source is. This area of study is very useful to understand mutiple phenomen, such as the temperature in a room or tumors. That is because the behaviour of the heat, which is known as thermal diffusivity , is always part of the nature. This instructional video is conducted by professor Cristián Warnken.

Young Capde researcher joins ICM seminar

Nicolás Varela, CAPDE postgraduate researcher, participated in the activity “Young people with Science” that was organized by Iniciativa Científico Milenio (ICM) and held in Concon, close to Valparaíso, on 26th and 27th November 2015. The meeting was aimed to think science  from an  interdisciplinary point of view in order to contribute to the development of the science in Chile  and how, at the same time, it can help to the country´s development.

“It was an interesting occasion to meet other students that are part of ICM. It was very useful to make social and professional contacts”, pointed out Varela, who currently is studying a Master in Mathematics at Universidad Federico Santa María (UFSM). His specialization areas are patterns of concetration, elliptic operators and structural analysis, specifically seismic insulation modelation.

During the activity, he showed a poster that describes and explains Capde´s work. “Attendees showed a great interested in the research that Capde is carrying out. Some of them also were surprised to know what can be made based on pure mathematics”, he added. As Varela, other young researchers belonging to more than 30 centers  made presentations.

As a result of the discussions, the creation of a governmental consulting entity in the field of the science and education programs addressed to the society were proposed.

ICM meets Capde´s members

The Factulty of Physical and Mathematical Science of Universidad de Chile received on 21th October 2015, the visit of Virginia Garretón and Soledad Hevia, Executive Director and communication analist of Iniciativa Cientítiva Milenio (ICM). They met Capde Capde´s members, including young and senior pr researchers, as well as staff.

Manuel del Pino, main researcher and National Science Award 2009, presented an overview of the center and the activities carried out to date, while focusing on strengths and weaknesses The gathering was also an opportunity to dialogue about challenges that faces science in Chile and how to expand media influence.

Capde participates in ICM 3D project

CAPDE joins this 3D project organized by Iniciativa Científico Milenio (ICM), which  consists on representing images through three dimensional technology. It will be soon available on website and applied for outreach activities. “This technology is very useful to make people to understand complex realities. It allows, for instance, to enter into a classroom, while the professor explains how mathematical modeling works”, said Fabián Castro, head of bussiness of the company that is developing this initiative.

November

Monday 16

16 hrs.

Matteo Rizzi (SISSA, Italy)

Clifford Tori and the singularly perturbed Cahn-Hilliard equation

Abstract

17hrs.

Panayotis Smyrnelis (CMM)

Connecting orbits of the system $u”=\nabla W(u)$

We will give necessary and sufficient conditions for the existence of
bounded minimal solutions of the system $u”=\nabla W(u)$. We will also
prove the existence of heteroclinic, homoclinic and periodic orbits in
analogy with the scalar case. Finally, we will mention new kinds of
connecting orbits that may occur in the vector case.

Thursday 26 – Saturday 28

SOMACHI (Pucón)

http://www.somachi.cl/encuentro2015

Monday 30

15hrs.

Nicolás Carreño (USM)

Insensitizing controls for the Boussinesq system with a reduced number of controls

Abstract

16hrs.

Felipe Barra (DFI, U. de Chile)
Termodinámica de sistemas cuánticos abiertos.
La evolución de sistemas cuánticos abiertos se puede describir, en muchos casos, con la ecuación de Lindblad. En particular la de algunos sistemas que operan como maquinas térmicas o refrigeradores de escala nanoscópica. Sin embargo, para estudiar las propiedades termodinámicas de estos dispositivos es necesario
entender como la interacción con el medio externo genera la descripción de Lindblad en cuestión. En esta charla discutiré dos escenarios frecuentemente usados para describir la interacción de un sistema con su medio ambiente junto con las diferencias (y confusiones)  que introducen en la descripción termodinámica.

October

Wednesday October 14

16hrs.

Søren Fournais (Aarhus University)

Optimal magnetic Sobolev constants in the semiclassical limit

Abstract Soeren

17hrs.

Matteo Cozzi (University of Milan)

Plane-like minimizers for a non-local Ginzburg-Landau-type energy in a periodic medium

Abstract Matteo

Monday October 19

4:00pm

Remy Rodiac  (PUC)

Ginzburg-Landau type problems with prescribed degrees on the boundary

In this talk we will introduce the Ginzburg-Landau equations with the
so-called semi-stiff boundary conditions. It corresponds to
prescribing the modulus of the unknown $u$ on the boundary, together
with its winding number. This is a model for superconductivity which
is intermediate between the full Ginzburg-Landau model with magnetic
field and the simplified Ginzburg-Landau model without magnetic field
but with a Dirichlet boundary data studied by Béthuel-Brézis-Hélein.
Since the winding number is not continuous for the weak convergence in
$H^{1/2}$, the direct method of calculus of variations fails. This is
a problem with lack of compactness and a bubbling phenomenon appears.
We will then give some existence or non existence results for
minimizers of the Ginzburg-Landau energy with prescribed degrees on
the boundary. In order to do this we are also led to study the
Dirichlet energy with the same type of boundary conditions and we make
a link with minimal surfaces in $R^3$.

5:00pm

Yannick Sire (Johns Hopkins University)
Bounds on eigenvalues on riemannian manifolds

I will describe several recent results with N. Nadirashvili where we
construct extremal metrics for eigenvalues on riemannian surfaces.
This involves the study of a Schrodinger operator. As an application,
one gets isoperimetric inequalities on the 2-sphere for the third
eigenvalue of the Laplace Beltrami operator.

September

Monday September 14

Rafael Benguria (PUC)

The Brezis-Nirenberg Problem on S^n, in spaces of fractional dimension

Abstract: We consider the nonlinear eigenvalue problem,

-\Delta_{\mathbb{S^n}} u = \lambda u + |u|^{4/(n-2)} u,

with $u \in H_0^1(\Omega)$, where $\Omega$ is a  geodesic ball in S^n.
In dimension 3, this problem was considered by  Bandle and Benguria.
For positive radial solutions of this problem one is led to an
ordinary differential equation (ODE) that still makes sense when n is
a real rather than a natural number. Here we consider precisely that
situation with 2<n<4. Our main result is that in this case one has a
positive solution if and only if $\lambda \ge -n(n-2)/4$ is such that

\frac{1}{4} [(2 \ell_2 +1)^2 – (n-1)^2] < \lambda < \frac{1}{4} [(2
\ell_1 +1)^2 – (n-1)^2]

where $\ell_1$ (respectively $\ell_2$) is the first positive value of
$\ell$ for which the associated Legendre function ${\rm P}_{\ell}^{(2-n)/2} (\cos\theta_1)$ (respectively ${\rm P}_{\ell}^{(n-2)/2} (\cos\theta_1)$) vanishes.

Wednesday September 30

(Sala 1 de la Facultad de Matemáticas de la PUC)

16hrs.

Paolo Caldiroli (Universitá di Torino)

Isovolumetric and isoperimetric inequalities for a class of
capillarity functionals

Abstract: Capillarity functionals are parameter invariant functionals
defined on classes of two-dimensional parametric surfaces in
$\mathbb{R}^{3}$ as the sum of the area integral and an anisotropic
term of suitable form. In the class of parametric surfaces with the
topological type of the sphere and with fixed volume, extremals of
capillarity functionals are surfaces whose mean curvature is
prescribed up to a constant. For a certain class of anisotropies
vanishing at infinity, we prove existence and nonexistence of
volume-constrained, spherical-type, minimal surfaces for the
corresponding capillarity functionals. Moreover, in some cases, we
show existence of extremals for the full isoperimetric inequality.

17hrs.

Denis Bonhere (Université Libre de Bruxelles)

On the higher dimensional Extended Allen-Cahn equation

Abstract: In this talk, I will present results on a fourth order
extension of Allen-Cahn in a bounded domain of R^N with Navier
boundary conditions or in the whole space. The diffusion is driven by
a combination of the bilaplacian and the laplacian. In striking
contrast with the classical AC, establishing the sign and the symmetry
(when the domain is symmetric) of solutions minimizing the associated
functional is not an easy task. For bounded solutions in R^N, I will
present rigidity and Liouville type results and in particular an
analogue of the Gibbons’ conjecture.
The talk is based on a joint work with J. Földes & A. Saldaña and
another one with F. Hamel.