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.


MondayApril 13, 2015
TimeDescriptionSpeakerLocationAbstractsSlides
8:30 - 8:55Limit Shapes Workshop Registration11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:45The limit shape of random SU(3) representationsDan Romik, University of California, Davis11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Stochastic quantum integrable systemsIvan Corwin, Columbia University11th Floor Lecture Hall
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11:30 - 12:15Solving interacting particle systems by Fourier-like transformsLeonid Petrov, University of Virginia11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch
2:30 - 3:15Limit shapes for interacting particle systems and their universal fluctuationsPatrick Ferrari, Rheinische Friedrich-Wilhelms-Universität Bonn11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Limit shapes in the Schur processDan Betea, Université de Paris VI (Pierre et Marie Curie)11th Floor Lecture Hall
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5:00 - 6:30Welcome Reception11th Floor Collaborative Space

TuesdayApril 14, 2015
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Circles in the SandLionel Levine, Cornell University11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15TBACharles Smart, Cornell University11th Floor Lecture Hall
11:30 - 12:15The limit shape of the Abelian Sandpile identityAndrea Sportiello, Université de Paris XIII (Paris-Nord), CNRS and LIPN11th Floor Lecture Hall
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12:30 - 2:00Break for Lunch
2:00 - 2:45Small-particle limits in a regularized Laplacian random growth modelAmanda Turner, University of Lancaster11th Floor Lecture Hall
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2:50 - 3:15SIR epidemics on random graphs with a given degree sequenceMalwina Luczak, Queen Mary University11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break1th Floor Collaborative Space
4:00 - 4:25The Shape of IceKari Eloranta, Aalto University11th Floor Lecture Hall
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4:30 - 4:55Perfect sampling algorithm for Schur processesMirjana Vuletic, University of Massachusetts11th Floor Lecture Hall
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WednesdayApril 15, 2015
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45An effective model of facets formation.Dimitry Ioffe, Technion-Israel Institute of Technology11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Asymptotic 'inner shape' of a deformed gradient Gibbs field.Roman Kotecky, University of Warwick11th Floor Lecture Hall
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11:30 - 12:15Height fluctuations in interacting dimersFabio Toninelli, Université Claude-Bernard (Lyon I)11th Floor Lecture Hall
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12:30 - 12:40Group Photo in Lecture Hall11th Floor Lecture Hall
12:40 - 2:00Break for Lunch
2:00 - 2:25Plane partitions with 2-periodic weightsSevak Mkrtchyan, University of Rochester11th Floor Lecture Hall
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2:30 - 2:55The full extremal process of the discrete Gaussian free field in 2D.Oren Louidor, Technion-Israel Institute of Technology11th Floor Lecture Hall
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3:00 - 4:15Poster Session and Coffee/Tea Break11th Floor Lecture Hall and Collaborative Space

ThursdayApril 16, 2015
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Escape from metastable states in Markovian systemsAlessandra Bianchi, Università di Padova11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Metastability and interface motion in disordered mediaThierry Bodineau, École Polytechnique11th Floor Lecture Hall
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11:30 - 12:15Subgaussian Rates of Convergence in First Passage PercolationKen Alexander, University of Southern California11th Floor Lecture Hall
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12:30 - 2:00Break for Lunch
2:00 - 2:25The Greedy Independent Set in a Random Graph with Given DegreesGraham Brightwell, London School of Economics and Political Science11th Floor Lecture Hall
2:30 - 3:15Gradient Gibbs measures with disorderCodina Cotar, University College London11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Central Limit Theorem for discrete log-gasesVadim Gorin, Massachusetts Institute of Technology11th Floor Lecture Hall
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FridayApril 17, 2015
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Shape continuity theorems in percolationEviatar Procaccia, University of California, Los Angeles11th Floor Lecture Hall
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10:00 - 10:45Statistical mechanics via asymptotics of symmetric functionsGreta Panova, University of Pennsylvania11th Floor Lecture Hall
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10:45 - 11:15Coffee/Tea Break11th Floor Collaborative Space
11:15 - 12:00The Z-invariant massive Laplacian on isoradial graphs.Beatrice deTiliere, Université de Paris VI (Pierre et Marie Curie)11th Floor Lecture Hall
12:15 - 1:00Arctic curves for the-six vertex model on generic domainsFilippo Colomo, National Institute of Nuclear Physics (INFN)11th Floor Lecture Hall
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1:00 - 2:30Break for Lunch
2:30 - 2:55Minimum mean weighted cycles on randomly weighted graphs.David Wilson, Microsoft Research11th Floor Lecture Hall
3:00 - 5:00Discussion11th Floor Lecture Hall and Collaborative Space