Organizing Committee
Abstract

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, such as 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.

Confirmed Speakers & Participants

Workshop Schedule

Monday, February 26, 2018
TimeEventLocationMaterials
8:30 - 8:55Registration121 South Main Street Providence RI 11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45The 2D Coulomb gas and the Gaussian free field - Paul Bourgade, NYU11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:00Statistical physics approach for one and two-dimensional log-gases - Thomas Leblé, Courant Institute of Mathematical Sciences11th Floor Lecture Hall
11:30 - 12:15Renormalized Energy Equidistribution and Local Charge Balance in Coulomb Systems - Simona Rota Nodari, Université de Bourgogne11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Dynamics of a planar Coulomb gas - Djalil Chafaï, Université Paris-Dauphine11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Concentration for Coulomb gases and Coulomb transport inequalities - Mylène Maïda, Université des Sciences et Technologies de Lille11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, February 27, 2018
TimeEventLocationMaterials
9:00 - 9:45The random landscape of spiked tensors - Gérard Ben Arous, NYU11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Spectral gap in bipartite biregular graphs and applications - Ioana Dumitriu, University of Washington11th Floor Lecture Hall
11:30 - 12:15Random Polynomial Mappings - Norman Levenberg, University of Indiana11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15The two periodic Aztec diamond - Arno Kuijlaars, KU Leuven11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Point distributions on the sphere - energy minimization, discrepancy, and more. - Dmitriy Bilyk, University of Minnesota11th Floor Lecture Hall
5:00 - 6:00Problem Sessions11th Floor Lecture Hall 
Wednesday, February 28, 2018
TimeEventLocationMaterials
9:00 - 9:45Gaussian Free Field in (self-adjoint) random matrices and random surfaces - Alexei Borodin, MIT11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Convolutions and fluctuations- free, finite, quantized - Vadim Gorin, MIT11th Floor Lecture Hall
11:30 - 12:15Universality for Discrete Beta models - Alice Guionnet, ENS de Lyon11th Floor Lecture Hall
12:30 - 12:40Workshop Group Photo11th Floor Lecture Hall 
12:40 - 2:15Break for Lunch / Free Time  
2:15 - 3:00Crystal problems for binary systems - Laurent Bétermin, University of Copenhagen11th Floor Lecture Hall
3:00 - 4:15Coffee/Tea Break11th Floor Collaborative Space 
4:15 - 5:00On some concrete criteria for quantum and stochastic confinement - Irina Nenciu, University of Illinois11th Floor Lecture Hall
6:30 - 8:00Public Lecture Sleeping Beauty and Other Probability Conundrums - Peter Winkler, Dartmouth  
Thursday, March 1, 2018
TimeEventLocationMaterials
9:00 - 9:45Two manifestations of rigidity in point sets- forbidden regions and maximal degeneracy - Subhro Ghosh, National University of Singapore11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Novel Computations with Random Matrix Theory and Julia - Alan Edelman, MIT11th Floor Lecture Hall
11:30 - 12:15Finite-range kernel decompositions and asymptotic Optimal Transport between configurations - Mircea Petrache, Pontificia Universidad Catolica de Chile11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Random matrices, operators and analytic functions - Benedek Valko, University of Wisconsin – Madison11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Random matrix limits via stochastic differential equations - Diane Holcomb, University of Arizona11th Floor Lecture Hall
5:00 - 5:45Convergence of spectral measures and eigenvalue rigidity in random matrices - Elizabeth Meckes, Case Western University11th Floor Lecture Hall
Friday, March 2, 2018
TimeEventLocationMaterials
9:00 - 9:45Random configurations with low energy - Carlos Beltrán, Universidad de Cantrabria (Spain)11th Floor Lecture Hall
10:00 - 10:45On the universal optimality of the 600-cell - the Levenshtein framework lifted - Peter Dragnev, Purdue University Fort Wayne11th Floor Lecture Hall
10:45 - 11:15Coffee/Tea Break11th Floor Collaborative Space 
11:15 - 12:00Asymptotic results for the polarization problem in the hypersingular case - Sergiy Borodachov, Towson University11th Floor Lecture Hall
12:15 - 1:45Break for Lunch / Free Time  
1:45 - 2:30Deterministic and non-deterministic Hyperuniformity in the compact setting - Johann Brauchart, Graz University of Technology11th Floor Lecture Hall
2:45 - 3:15Coffee/Tea Break11th Floor Collaborative Space 
3:15 - 4:15Mean-Field limits for Coulomb dynamics - Sylvia Serfaty, Courant Institute of Mathematical Science a Joint lecture with Brown University PDE seminar11th Floor Lecture Hall

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Associated Semester Workshops

Lecture Videos

Random configurations with low energy

Carlos Beltran
Universidad de Cantrabria (Spain)
March 2, 2018

Random matrices, operators and analytic functions

Benedek Valko
University of Wisconsin - Madison
March 1, 2018

Crystal problems for binary systems

Laurent Bétermin
University of Copenhagen
February 28, 2018

Random Polynomial Mappings

Norman Levenberg
University of Indiana
February 27, 2018

Concentration for Coulomb gases and Coulomb transport inequalities

Mylène Maïda
Université des Sciences et Technologies de Lille
February 26, 2018

Dynamics of a planar Coulomb gas

Djalil Chafaï
Université Paris-Dauphine
February 26, 2018

Statistical physics approach for one and two-dimensional log-gases

Thomas Leblé
Courant Institute of Mathematical Sciences
February 26, 2018