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)
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Description

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 Alexander Razborov (Chicago)
  • Multipodal phases in graphs by Lorenzo Sadun (Austin)
  • Nonequilibrium solids by Giulio Biroli (CEA-Saclay)
  • Other transitions by Remi Monasson (ENS-Paris)


MondayFebruary 9, 2015
TimeDescriptionSpeakerLocationAbstractsSlides
8:30 - 8:55Registration11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:10Theme of workshopCharles Radin, University of Texas11th Floor Lecture Hall
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9:10 - 10:10Densest packing of, and on, Euclidean spheresNoam Elkies, Harvard University 11th Floor Lecture Hall
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10:10 - 10:40Discussion Period11th Floor Lecture Hall
10:40 - 11:10Coffee/Tea Break11th Floor Collaborative Space
11:10 - 12:10Impromptu Discussion of Statistical FormalismCharles Radin, University of Texas11th Floor Lecture Hall
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12:10 - 12:40Discussion Period11th Floor Lecture Hall
12:40 - 2:20Break for Lunch
2:20 - 3:00The role of symmetry in sphere packing in high dimensionsHenry Cohn, Microsoft (New England)11th Floor Lecture Hall
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3:00 - 3:30Short Break
3:30 - 4:10The fluid-solid phase transition on a curved surfaceVinothan Manoharan, Harvard University 11th Floor Lecture Hall
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4:30 - 6:00Welcome Reception11th Floor Collaborative Space

TuesdayFebruary 10, 2015
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 10:00Syntactic methods in continuous combinatoricsAlexander Razborov, University of Chicago11th Floor Lecture Hall
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10:00 - 10:30Discussion Period11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break11th Floor Collabortive Space
10:30 - 11:50Statistical Mechanics and Combinatorics (ongoing semester course)Richard Kenyon, Brown University10th Floor Classroom
11:00 - 12:00Multipodal phases in graphsLorenzo Sadun, University of Texas11th Floor Lecture Hall
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12:00 - 12:30Discussion Period11th Floor Lecture Hall
12:30 - 2:10Break for Lunch
2:10 - 2:40Fixed-energy harmonic functionsRichard Kenyon, Brown University 11th Floor Lecture Hall
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2:40 - 2:50Short Break
2:50 - 3:20Harmonic pinnacles in the discrete Gaussian modelEyal Lubetzky, New York University 11th Floor Lecture Hall
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3:20 - 3:50Coffee/Tea Break11th Floor Collaborative Space
3:50 - 4:20Random walk on the random graphYuval Peres, Microsoft (Redmond)11th Floor Lecture Hall
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4:20 - 4:30Short Break
4:30 - 5:00Various types of phase transitions in extremal graph theoryMiklos Simonovits, Hungarian Academy of Sciences11th Floor Lecture Hall
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WednesdayFebruary 11, 2015
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 10:00Non-equilibrium solidsGiulio Biroli, CEA Saclay11th Floor Lecture Hall
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10:00 - 10:30Discussion Period11th Floor Lecture Hall
10:30 - 10:50Coffee/Tea Break11th Floor Collaborative Space
10:50 - 11:50Aperiodic tilingsBoris Solomyak, University of Washington11th Floor Lecture Hall
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11:50 - 12:20Discussion Period11th Floor Lecture Hall
12:20 - 1:40Break for Lunch
1:40 - 2:10Poster Session11th Floor Lecture Hall and Collabortive Space
2:10 - 2:40How the Ising crystal growsSenya Shlosman, Aix-Marseille University11th Floor Lecture Hall
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2:40 - 2:50Short Break
2:50 - 3:20Characterizing extremal limitsOleg Pikhurko, University of Warwick11th Floor Lecture Hall
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3:20 - 3:50Coffee/Tea Break11th Floor Collaborative Space
3:50 - 4:20Universal behavior near Erdoes-RenyiLorenzo Sadun, University of Texas11th Floor Lecture Hall
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4:20 - 4:30Short Break
4:30 - 5:00Problems on convergent sequences of dense graphsVera Sos, Hungarian Academy of Sciences11th Floor Lecture Hall
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ThursdayFebruary 12, 2015
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 10:00Other transitions in statistical physics and beyond- from the liquid-gas transition to the representation of space in the brainRemi Monasson, Ecole Normale Superieure (Paris)11th Floor Lecture Hall
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10:00 - 10:30Discussion Period11th Floor Lecture Hall
10:30 - 11:50Statistical Mechanics and Combinatorics (ongoing semester course)Richard Kenyon, Brown University10th Floor Classroom
11:00 - 12:00The Phases of Hard Sphere SystemsVeit Elser, Cornell University
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12:00 - 12:30Discussion Period11th Floor Lecture Hall
12:30 - 2:10Break for Lunch
2:10 - 2:40Phase transitions in models of quasicrystalsDavid Aristoff, Colorado State University11th Floor Lecture Hall
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2:40 - 2:50Short Break
2:50 - 3:20Asymptotics for sparse exponential graph modelsMei Yin, University of Denver11th Floor Lecture Hall
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3:00 - 3:10Post Doc & Grad Student Group Photos11th Floor Lecture Hall
3:20 - 3:25Workshop Group Photo11th Floor Lecture Hall
3:25 - 3:50Coffee/Tea Break11th Floor Collaborative Space
3:50 - 4:20Lattices, packings and energy minimizationAbhinav Kumar, SUNY Stony Brook11th Floor Lecture Hall
4:20 - 4:30Short Break
4:30 - 5:00Large deviations in random graphsYufei Zhao, Massachusetts Institute of Technology11th Floor Lecture Hall
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FridayFebruary 13, 2015
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 10:30Discussion PeriodTopics determined from previous talks11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break11th Floor Lecture Hall
11:00 - 12:30Discussion PeriodTopics determined from previous talks11th Floor Lecture Hall
12:30 - 2:10Break for Lunch
2:10 - 2:40L^p theory of sparse graph limitsJennifer Chayes, Microsoft (New England)11th Floor Lecture Hall
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2:40 - 2:50Short Break
2:50 - 3:20Applications of L^p theory of sparse graph limitsChristian Borgs, Microsoft (New England)11th Floor Lecture Hall
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3:20 - 3:50Coffee/Tea Break11th Floor Collaborative Space
3:50 - 4:20Phase transitions in tilings constructed from stationary fusion rulesNatalie Frank, Vassar College11th Floor Lecture Hall
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4:30 - 5:00Crystallization of hard shapes- from disks to tetrahedraMichael Engel, University of Michigan11th Floor Lecture Hall