Optimal and Random Point Configurations
(February 26 – March 2, 2018)

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Description

This workshop will focus on probabilistic and physical aspects of systems of interacting points: their statistical mechanics, phase transitions, and ground states. Such systems include random point processes arising in probability and statistical physics in the study of random matrices, determinantal processes, zeros of random polynomials, disordered ground states, and hyperuniform systems as well as configurations satisfying a geometric or analytic optimality constraint. Special cases also involve disordered and ordered sphere packings and covering problems.

While systems of interacting particles, their free energy and crystallization properties have been studied for a long time in the statistical physics community, there has also been much activity recently, both in the random matrix community and probability communities and in the complex analysis community to understand the microscopic laws of eigenvalues of random matrices and points in beta-ensembles, as well as understanding and quantifying the rigidity of related random point processes and obtaining explicit formulas for correlation functions. Large point sets with quantifiable distribution properties have long played an important role also in approximation, numerical integration, and coding theory. All these communities are seldom mixing, while these topics also link with globally and locally optimal point configurations that arise in approximation theory, including their crystallization properties. A central objective would thus be to connect the probability, statistical physics, mathematical physics and approximation theory communities.

Organizing Committee

= speaker    = poster presenter

Monday February 26, 2018
Time Description Speaker Location Abstracts Slides
8:30 - 8:55Registration121 South Main Street Providence RI 11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:45The 2D Coulomb gas and the Gaussian free fieldPaul Bourgade, NYU11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break 11th Floor Collaborative Space
10:30 - 11:00Statistical physics approach for one and two-dimensional log-gasesThomas Leblé, Courant Institute of Mathematical Sciences11th Floor Lecture Hall
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11:30 - 12:15Renormalized Energy Equidistribution and Local Charge Balance in Coulomb SystemsSimona Rota Nodari, Université de Bourgogne11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch / Free Time
2:30 - 3:15Dynamics of a planar Coulomb gasDjalil Chafaï, Université Paris-Dauphine11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break 11th Floor Collaborative Space
4:00 - 4:45Concentration for Coulomb gases and Coulomb transport inequalitiesMylène Maïda, Université des Sciences et Technologies de Lille11th Floor Lecture Hall
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5:00 - 6:30Welcome Reception11th Floor Collaborative Space

Tuesday February 27, 2018
Time Description Speaker Location Abstracts Slides
9:00 - 9:45The random landscape of spiked tensorsGérard Ben Arous, NYU11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break 11th Floor Collaborative Space
10:30 - 11:15Spectral gap in bipartite biregular graphs and applicationsIoana Dumitriu, University of Washington11th Floor Lecture Hall
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11:30 - 12:15Random Polynomial MappingsNorman Levenberg, University of Indiana11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch / Free Time
2:30 - 3:15The two periodic Aztec diamondArno Kuijlaars, KU Leuven11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break 11th Floor Collaborative Space
4:00 - 4:45Point distributions on the sphere - energy minimization, discrepancy, and more.Dmitriy Bilyk, University of Minnesota11th Floor Lecture Hall
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5:00 - 6:00Problem Sessions11th Floor Lecture Hall

Wednesday February 28, 2018
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Gaussian Free Field in (self-adjoint) random matrices and random surfacesAlexei Borodin, MIT11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break 11th Floor Collaborative Space
10:30 - 11:15Convolutions and fluctuations- free, finite, quantizedVadim Gorin, MIT11th Floor Lecture Hall
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11:30 - 12:15Universality for Discrete Beta modelsAlice Guionnet, ENS de Lyon11th Floor Lecture Hall
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12:30 - 12:40Workshop Group Photo11th Floor Lecture Hall
12:40 - 2:15Break for Lunch / Free Time
2:15 - 3:00Crystal problems for binary systemsLaurent Bétermin, University of Copenhagen11th Floor Lecture Hall
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3:00 - 4:15Poster Session Coffee/Tea Break 11th Floor Collaborative Space
4:15 - 5:00On some concrete criteria for quantum and stochastic confinementIrina Nenciu, University of Illinois11th Floor Lecture Hall
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6:30 - 8:00Public Lecture: Sleeping Beauty and Other Probability ConundrumsPeter Winkler, Dartmouth

Thursday March 1, 2018
Time Description Speaker Location Abstracts Slides
10:30 - 11:15Novel Computations with Random Matrix Theory and JuliaAlan Edelman, MIT11th Floor Lecture Hall
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11:30 - 12:15Finite-range kernel decompositions and asymptotic Optimal Transport between configurationsMircea Petrache, Pontificia Universidad Catolica de Chile11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch / Free Time
2:30 - 3:15Random matrices, operators and analytic functionsBenedek Valko, University of Wisconsin – Madison11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break 11th Floor Collaborative Space
4:00 - 4:45Random matrix limits via stochastic differential equationsDiane Holcomb, University of Arizona11th Floor Lecture Hall
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5:00 - 5:45Convergence of spectral measures and eigenvalue rigidity in random matricesElizabeth Meckes, Case Western University11th Floor Lecture Hall
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Friday March 2, 2018
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Random configurations with low energyCarlos Beltrán, Universidad de Cantrabria (Spain)11th Floor Lecture Hall
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10:00 - 10:45On the universal optimality of the 600-cell - the Levenshtein framework liftedPeter Dragnev, Purdue University Fort Wayne11th Floor Lecture Hall
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10:45 - 11:15Coffee/Tea Break 11th Floor Collaborative Space
11:15 - 12:00Asymptotic results for the polarization problem in the hypersingular caseSergiy Borodachov, Towson University11th Floor Lecture Hall
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12:15 - 1:45Break for Lunch / Free Time
1:45 - 2:30Deterministic and non-deterministic Hyperuniformity in the compact settingJohann Brauchart, Graz University of Technology11th Floor Lecture Hall
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2:45 - 3:15Coffee/Tea Break 11th Floor Collaborative Space
3:15 - 4:15Mean-Field limits for Coulomb dynamicsSylvia Serfaty, Courant Institute of Mathematical Science a Joint lecture with Brown University PDE seminar11th Floor Lecture Hall
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