Monday May 7, 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.

5.00pm  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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Monday May 28, 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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Monday June 11, 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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#### Past Seminars

“Longtime Behaviour of Nonlinear Waves”,  June 8-12, Bielefeld University, Bielefend, Germany. (Claudio Muñoz).

“Inverse Problems in the Physical Sciences”, August 3-5, Santiago, Chile. (Claudio Muñoz).

“II-Workshop in Nonlinear Dispersive Equations”, Octubre 6-9, Campinas, Sao Paulo, Brazil. (Claudio Muñoz).

“New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems” October 19 – 30, MSRI, Berkeley, California, USA. (Claudio Muñoz).

“3rd Chile-Japan Workshop on Nonlinear PDEs”,  December 8 -11, Osaka University, Osaka, Japan. (Claudio Muñoz).

“Nonlinear elasticity and fractures”, June 23-24, Pontificia Universidad Católica de Chile, Santiago, Chile. (Duván Henao).

The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications. July 1 – July 5, 2016, Orlando, Florida, USA. (C. Muñoz, F. Mahmoudi, I. Guerra).

“International Conference On Local and non local Partial Differential Equations”, April 24 – 26, New York University Shanghai, China. (Mónica Musso).

“Recent Trends and Geometric Analysis”, June 1-5, Marseille, France. (Mónica Musso).

TBA

#### Past Events

MathAmSud project EEQUADD (Nonlinear and Fractional Evolution EQUAtions: Dispersion, Dynamics, well-posedness and Functional Analytic tools)”, CMM, Universidad de Chile, December  4-7 , 2017.

First Belgium-Chile-Italy Conference en PDE’s”, Université Libre de Bruxelles, Belgium, November  13-17 , 2017.

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

2nd. Workshop on Nonlinear Evolution Equations”,  Universidad Austral de Chile, Valdivia, December 12-16 2016.

Third Sino-Chilean Conference on Nonlinear Partial Differential Equations and Nonlinear Analysis, December 9-12 2016, Wuhan, China.

CAPDE School on Nonlinear Partial Differential Equations, September 28-October 5, 2016.

Conference on Nonlinear Elliptic PDEs at the End of the World, Universidad de Magallanes, Punta Arenas, Chile, March 2-6, 2015.

Third Chile Japan Workshop on Nonlinear PDEs, Osaka University, Japan. December 8-11, 2015