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 Events
Courant Institute, NYU
Fri 1 Dec 2017, 3:00pm SPECIAL
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium--Microscopic description of Coulomb-type systems
ESB 2012
Fri 1 Dec 2017, 3:00pm-4:00pm

Abstract

 
 

Systems of points with Coulomb, logarithmic (or more generally inverse powers of the distance) interactions arise in various settings: an instance is the classical Coulomb gas which in some cases happens to be a random matrix ensemble, another is vortices in the Ginzburg-Landau model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. After reviewing the motivations, we will take a point of view based on the detailed expansion of the interaction energy to describe the microscopic behavior of the systems and its statistical mechanics. In particular a Central Limit Theorem for fluctuations and a Large Deviations Principle for the microscopic point processes are given. This allows to observe the effect of the temperature as it gets very large or very small, and to connect with crystallization questions.

The main results are joint with Thomas Leblé and also based on previous works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.

Note for Attendees

Light refreshments will be served at 2:45pm in ESB 4133, the PIMS Lounge before this colloquium.
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Université Paris-Saclay
Fri 1 Dec 2017, 5:00pm SPECIAL
ESB 2012
UBC Mathematics Lecture Series: Regularized Optimal Transport. Part II
ESB 2012
Fri 1 Dec 2017, 5:00pm-6:30pm

Details

 Optimal transport theory provides practitioners from statistics, imaging, graphics or machine learning with a very powerful toolbox to compare probability measures. These tools translate however in their original form into computational schemes that can become intractable or suffer from instability (such as non-differentiability or estimation bias). We will present in these two lectures how a few insights from optimization theory and in particular a careful regularization can result in tools that are considerably easier to implement, run faster because they can take advantage of parallel hardware and behave better from a statistical perspective. We will highlight applications from diverse areas, from graphics and brain imaging to text analysis and parametric estimation.

Note for Attendees

 This is the second of a two part lecture. The first part will be given on Nov 30 2017, in ESB 2012 at the same time. Details for Part I are available here.
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