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.

Image for "Optimal and Random Point Configurations"

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, February 26, 2018
TimeEventLocationMaterials
8:30 - 8:55am ESTRegistration121 South Main Street Providence RI 11th Floor Collaborative Space 
8:55 - 9:00am ESTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45am ESTThe 2D Coulomb gas and the Gaussian free field - Paul Bourgade, NYU11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:00am ESTStatistical physics approach for one and two-dimensional log-gases - Thomas Leblé, Courant Institute of Mathematical Sciences11th Floor Lecture Hall
11:30 - 12:15pm ESTRenormalized Energy Equidistribution and Local Charge Balance in Coulomb Systems - Simona Rota Nodari, Université de Bourgogne11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch / Free Time  
2:30 - 3:15pm ESTDynamics of a planar Coulomb gas - Djalil Chafaï, Université Paris-Dauphine11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm ESTConcentration for Coulomb gases and Coulomb transport inequalities - Mylène Maïda, Université des Sciences et Technologies de Lille11th Floor Lecture Hall
5:00 - 6:30pm ESTWelcome Reception11th Floor Collaborative Space 
Tuesday, February 27, 2018
TimeEventLocationMaterials
9:00 - 9:45am ESTThe random landscape of spiked tensors - Gérard Ben Arous, NYU11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTSpectral gap in bipartite biregular graphs and applications - Ioana Dumitriu, University of Washington11th Floor Lecture Hall
11:30 - 12:15pm ESTRandom Polynomial Mappings - Norman Levenberg, University of Indiana11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch / Free Time  
2:30 - 3:15pm ESTThe two periodic Aztec diamond - Arno Kuijlaars, KU Leuven11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm ESTPoint distributions on the sphere - energy minimization, discrepancy, and more. - Dmitriy Bilyk, University of Minnesota11th Floor Lecture Hall
5:00 - 6:00pm ESTProblem Sessions11th Floor Lecture Hall 
Wednesday, February 28, 2018
TimeEventLocationMaterials
9:00 - 9:45am ESTGaussian Free Field in (self-adjoint) random matrices and random surfaces - Alexei Borodin, MIT11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTConvolutions and fluctuations- free, finite, quantized - Vadim Gorin, MIT11th Floor Lecture Hall
11:30 - 12:15pm ESTUniversality for Discrete Beta models - Alice Guionnet, ENS de Lyon11th Floor Lecture Hall
12:30 - 12:40pm ESTWorkshop Group Photo11th Floor Lecture Hall 
12:40 - 2:15pm ESTBreak for Lunch / Free Time  
2:15 - 3:00pm ESTCrystal problems for binary systems - Laurent Bétermin, University of Copenhagen11th Floor Lecture Hall
3:00 - 4:15pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:15 - 5:00pm ESTOn some concrete criteria for quantum and stochastic confinement - Irina Nenciu, University of Illinois11th Floor Lecture Hall
6:30 - 8:00pm ESTPublic Lecture Sleeping Beauty and Other Probability Conundrums - Peter Winkler, Dartmouth  
Thursday, March 1, 2018
TimeEventLocationMaterials
9:00 - 9:45am ESTTwo manifestations of rigidity in point sets- forbidden regions and maximal degeneracy - Subhro Ghosh, National University of Singapore11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTNovel Computations with Random Matrix Theory and Julia - Alan Edelman, MIT11th Floor Lecture Hall
11:30 - 12:15pm ESTFinite-range kernel decompositions and asymptotic Optimal Transport between configurations - Mircea Petrache, Pontificia Universidad Catolica de Chile11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch / Free Time  
2:30 - 3:15pm ESTRandom matrices, operators and analytic functions - Benedek Valko, University of Wisconsin – Madison11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm ESTRandom matrix limits via stochastic differential equations - Diane Holcomb, University of Arizona11th Floor Lecture Hall
5:00 - 5:45pm ESTConvergence of spectral measures and eigenvalue rigidity in random matrices - Elizabeth Meckes, Case Western University11th Floor Lecture Hall
Friday, March 2, 2018
TimeEventLocationMaterials
9:00 - 9:45am ESTRandom configurations with low energy - Carlos Beltrán, Universidad de Cantrabria (Spain)11th Floor Lecture Hall
10:00 - 10:45am ESTOn the universal optimality of the 600-cell - the Levenshtein framework lifted - Peter Dragnev, Purdue University Fort Wayne11th Floor Lecture Hall
10:45 - 11:15am ESTCoffee/Tea Break11th Floor Collaborative Space 
11:15 - 12:00pm ESTAsymptotic results for the polarization problem in the hypersingular case - Sergiy Borodachov, Towson University11th Floor Lecture Hall
12:15 - 1:45pm ESTBreak for Lunch / Free Time  
1:45 - 2:30pm ESTDeterministic and non-deterministic Hyperuniformity in the compact setting - Johann Brauchart, Graz University of Technology11th Floor Lecture Hall
2:45 - 3:15pm ESTCoffee/Tea Break11th Floor Collaborative Space 
3:15 - 4:15pm ESTMean-Field limits for Coulomb dynamics - Sylvia Serfaty, Courant Institute of Mathematical Science a Joint lecture with Brown University PDE seminar11th Floor Lecture Hall

Associated Semester Workshops

Lecture Videos

Random configurations with low energy

Carlos Beltran
Universidad de Cantabria (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

Mylene Maida
Université des Sciences et Technologies de Lille
February 26, 2018

Dynamics of a planar Coulomb gas

Djalil Chafai
Universite Paris-Dauphine
February 26, 2018

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

Thomas Leble
Courant Institute of Mathematical Sciences
February 26, 2018