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Limit shapes (April 13-17, 2015)


Organizing Committee
  • Marek Biskup
    (University of California, Los Angeles)
  • Alexei Borodin
    (MIT)
  • Béatrice de Tilière
    (Université Pierre et Marie Curie, Paris 6)
  • Richard Kenyon
    (Brown University)
  • Senya Shlosman
    (Aix-Marseille University)

Description

Since the days of Boltzmann, it has been well accepted that natural phenomena, when described using tools of statistical mechanics, are governed by various "laws of large numbers." For practitioners of the field this usually means that certain empirical means converge to constants when the limit of a large system is taken. However, evidence has been amassed that such laws apply also to geometric features of these systems and, in particular, to many naturally-defined shapes. Earlier examples where such convergence could be proved include certain interacting particle systems, invasion percolation models and spin systems in equilibrium statistical mechanics.

The last decade has seen a true explosion of "limit-shape" results. New tools of combinatorics, random matrices and representation theory have given us new models for which limit shapes can be determined and further studied: dimer models, polymer models, sorting networks, ASEP (asymmetric exclusion processes), sandpile models, bootstrap percolation models, polynuclear growth models, etc. The goal of the workshop is to attempt to confront this "ZOO" of combinatorial examples with older foundational work and develop a better understanding of the general limit shape phenomenon.


  • David Aristoff
    (University of Minnesota)
  • Marek Biskup
    (University of California, Los Angeles)
  • Mark Bowick
    (Syracuse University)
  • Michael Brenner
    (Harvard University)
  • Graham Brightwell
    (London School of Economics and Political Science)
  • Ivan Corwin*
    (Massachusetts Institute of Technology)
  • Amir Dembo
    (Stanford University)
  • Béatrice de Tilière
    (Université de Paris VI (Pierre et Marie Curie))
  • Persi Diaconis
    (Stanford University)
  • Hugo Duminil-Copin
    (University of Geneva)
  • Patrik Ferrari*
    (Rheinische Friedrich-Wilhelms-Universität Bonn)
  • Vadim Gorin*
    (Massachusetts Institute of Technology)
  • Tyler Helmuth
    (University of British Columbia)
  • Ander Holroyd
    (Microsoft Research)
  • Richard Kenyon
    (Brown University)
  • Abhinav Kumar
    (Massachusetts Institute of Technology)
  • Robert Kusner
    (University of Massachusetts)
  • Marcin Lis
    (Vrije Universiteit Amsterdam)
  • Malwina Luczak
    (Queen Mary and Westfield College)
  • Fabio Martinelli
    (Consiglio Nazionale delle Ricerche (CNR))
  • Sevak Mkrtchyan
    (Carnegie Mellon University)
  • Greta Panova*
    (University of California, Los Angeles)
  • Robin Pemantle
    (University of Pennsylvania)
  • Yuval Peres
    (Microsoft Research)
  • Charles Radin
    (University of Texas at Austin)
  • Emily Russell
    (Harvard University)
  • Lorenzo Sadun *
    (University of Texas at Austin)
  • Senya Shlosman
    (Aix-Marseille University)
  • Vladas Sidoravicius
    (Institute of Pure and Applied Mathematics (IMPA))
  • Jeff Steif
    (Chalmers University of Technology)
  • Daniel Stein
    (New York University)
  • Jessica Striker
    (University of Minnesota)
  • Cristina Toninelli
    (Université de Paris VII (Denis Diderot) et Université de Paris VI (Pierre et Marie Curie))
  • Mirjana Vuletic
    (University of Massachusetts)
  • Xuan Wang
    (University of North Carolina)
  • Samuel Watson
    (Massachusetts Institute of Technology)
  • Peter Winkler
    (Dartmouth College)