Crystals, Quasicrystals and Random Networks (Feb 9-13, 2015)

Organizing Committee
  • Mark Bowick
    (Syracuse University)
  • Persi Diaconis
    (Stanford University)
  • Charles Radin
    (University of Texas, Austin)
  • Peter Winkler
    (Dartmouth College)

The densest packing of unit disks in the plane is easily seen to be highly symmetric. This is exploited in statistical mechanics in arguing that as the density parameter is decreased from its optimum most packings at fixed density remain quite orderly (`solid'), changing only gradually until at a specific density they suddenly begin to `melt' into the disordered (`fluid') packings of low density. This workshop will explore two variants of this fundamental phenomenon. One variant concerns packings of special shapes, such as the Penrose kites and darts of the accompanying figure, whose densest packings are aperiodic tilings. The other concerns complex networks for which the optima are certain extremal graphs. These optimization problems, and especially their associated solid phases and solid/fluid phase transitions, are the subject of the workshop.

In summary, our workshop will explore two optimization problems on which there is active mathematical research. It will then focus on their associated solid phases and solid/fluid phase transitions which, on the contrary, are in dire need of mathematical clarification/understanding. It is hoped that progress can be made by pooling the expertise of researchers interested in various versions of this phenomenon. To promote cross-disciplinary information flow between the participants, the workshop format will have long tutorial/discussion sessions in the mornings, and short, more specialized talks in the afternoons.

The following tutorial/discussion sessions have been arranged so far:

  • Densest packings by Noam Elkies (Harvard)
  • Aperiodic tilings by Boris Solomyak (Washington)
  • Phases from hard spheres by Veit Elser (Cornell)
  • Extremal graphs by Sasha Razborov (Chicago)
  • Multipodal phases in graphs by Lorenzo Sadun (Austin)
  • Nonequilibrium solids by Giulio Biroli (CEA-Saclay)
  • Other transitions by Remi Monasson (ENS-Paris)

  • David Aristoff
    (University of Minnesota)
  • Jean Bellissard
    (Georgia Institute of Technology)
  • Giulio Biroli*
    (Commissariat à l'Énergie Atomique (CEA))
  • Marek Biskup
    (University of California, Los Angeles)
  • Christian Borgs *
    (Microsoft Research)
  • Mark Bowick *
    (Syracuse University)
  • Michael Brenner
    (Harvard University)
  • Sourav Chatterjee *
    (Stanford University)
  • Jennifer Chayes *
    (Microsoft Research)
  • Henry Cohn *
    (Microsoft Research)
  • 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)
  • Noam Elkies *
    (Harvard University)
  • Veit Elser*
    (Cornell University)
  • Vadim Gorin
    (Massachusetts Institute of Technology)
  • Tyler Helmuth
    (University of British Columbia)
  • Ander Holroyd
    (Microsoft Research)
  • Sabine Jansen
    (Ruhr-Universität Bochum)
  • Richard Kenyon *
    (Brown University)
  • Roman Kotecky*
    (University of Warwick)
  • Abhinav Kumar *
    (Massachusetts Institute of Technology)
  • Robert Kusner
    (University of Massachusetts)
  • Marcin Lis
    (Vrije Universiteit Amsterdam)
  • Oren Louidor
    (Technion-Israel Institute of Technology)