Lunes 7 de Mayo de 2018
Sala de Seminarios Felipe Álvarez Daziano 5to piso del DIM
4.10pm Mircea Petrache (PUC, Chile)
Title: Asymptotics for Optimal Transport between N-ples of points, with cost given by electrostatic interaction energy

Abstract: Consider the optimal transport problem N-ples of points, in which the transport cost between N points equals an electrostatic-type energy such as $\sum_{i\neq j} |x_i-x_j|^{-s}$ with $0<s<d$. We are led to a minimization problem for probability measures on $(\mathbb R^d)^N$, which is an N-marginal Optimal Transport problem, and has a direct physical interpretation.

We prove the sharp large-N asymptotics for the above N-marginal transport problem at second order, namely beyond the mean-field continuum limit. To this aim we establish a general finite-range decomposition technique into positive-definite contributions, extending a paper by Fefferman from 1985. This kind of decomposition seems interesting to study in itself and may have further applications.

Our questions also appear in Density Functional Theory, an important model used in computational chemistry and material science (1998 Nobel prize for W. Kohn). Mathematically, our problem represents a link between the study of ground states for classical and quantum gases. The techniques of the proof give a new viewpoint on wavelet-type decompositions, here applied within optimal transport theory.
Our description of asymptotics (a) can also be seen as an Optimal Transport parallel to, and (b) gives a new angle on, the study of asymptotics for Coulomb and Riesz gases, as done by Serfaty and collaborators.

5.pm  Amal Taarabt (PUC, Chile.)
Title: On the current-current correlation measure for random Schrödinger operators

Abstract:  We review various properties of random Schrödinger operators and recall formulations of conductivity and current-current correlation measure. In this talk we will present a panoramic view and recent results on localized regime. We will focus in particular on the diagonal behaviour problem of the ccc-measure and explain how it is related to the localization length.

This is a work in progress with J. Bellissard and G. De Nettis.
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Lunes 28 de Mayo de 2018
Sala de Seminarios Felipe Álvarez Daziano 5to piso del DIM
4.10pm Frédéric Rousset (Université Paris Sud, France)
Title: TBA
Abstract: TBA
5.pm  Claire Delplancke (CMM)
Title: TBA
Abstract: TBA
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Lunes  11 de Junio de 2018
Sala de Seminarios Felipe Álvarez Daziano 5to piso del DIM
4.10pm Erwin Topp (USACH, Chile)
Title: TBA
Abstract: TBA
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Seminarios Anteriores

 

 

  “Comportamiento Sostenido de Ondas No Lineales”,  Junio 8-12, Bielefeld University, Bielefend, Germany. (Claudio Muñoz).

  “Problemas Inversos en las Ciencias Físicas”, Agosto 3-5, Santiago, Chile. (Claudio Muñoz).

 “II-Taller en Ecuaciones Dispersivas No Lineales”, Octubre 6-9, Campinas, Sao Paulo, Brazil. (Claudio Muñoz).

 “Nuevos Retos en EPD: Dinámicas Deterministas y aleatoriedad en sistemas dimensionales altos e infinitos” Octubre 19 – 30, MSRI, Berkeley, California, USA. (Claudio Muñoz).

“Tercer Taller Chile-Japón en EPD No Lineales”, Diciembre 8 -11, Osaka University, Osaka, Japan. (Claudio Muñoz).

“Elasticidad y Fracturas No Lineales”, June 23-24, Pontificia Universidad Católica de Chile, Santiago, Chile. (Duván Henao).

“Conferencia Internacional en Ecuaciones Parciales Diferenciales Locales y No Locales”, Abril 24 – 26, New York University Shanghai, China. (Mónica Musso).

“Tendencias Recientes en Análisis Geométrico”, June 1-5, Marseille, France. (Mónica Musso).

Eventos futuros

TBA
Eventos pasados

MathAmSud project EEQUADD (Nonlinear and Fractional Evolution EQUAtions: Dispersion, Dynamics, well-posedness and Functional Analytic tools)”, CMM, Universidad de Chile, 4-7 de Diciembre de 2017.
Primera Conferencia Bélgica-Chile-Italia en PDE’s”, Université Libre de Bruxelles, Belgica,  13-17 de Noviembre, 2017.

Variational Models of Soft Matter”, Pontificia Universidad Católica de Chile, Santiago, 9-13 de Enero de 2017.

2do taller sobre ecuaciones de evolución no lineales,  Universidad Austral de Chile, Valdivia,  12-16 de Diciembre de 2016.

Tercera Conferencia chino-chilena sobre Ecuaciones Diferenciales Parciales No Lineales y Análisis no Lineal, 9-12 de Diciembre de 2016, Wuhan, China.

Escuela CAPDE. Ecuaciones diferenciales parciales no lineales. Fechas 28 de septiembre al 5 de octubre de 2016.

 Conferencia sobre EDPs elípticas no lineales en el Fin del Mundo, Universidad de Magallanes, Punta Arenas, Chile, Marzo 2-6, 2015.

El Tercer Taller Chile-Japón el PDEs no lineales, Osaka University, Japan. Deciembre 8-11, 2015.