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Integrability and Cluster Algebras: Geometry and Combinatorics (August 25-29, 2014)


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Review of applications will begin on April 15, 2014
Organizing Committee
  • Vladimir Fock
    Université de Strasbourg I (Louis Pasteur)
  • Max Glick
    University of Minnesota
  • Olga Kravchenko
    Institut Camille Jordan, Université Lyon 1
  • Sophie Morier-Genoud
    Université de Paris VI (Pierre et Marie Curie)
  • Valentin Ovsienko
    Institut Camille Jordan, Université Lyon 1
  • Rich Schwartz
    Brown University


Picture

[Image Courtesy of Rich Schwartz, Brown University]

 

Description

This workshop focuses on certain kinds of discrete dynamical systems that are integrable and have interpretations in terms of cluster algebras. Some such systems, like the pentagram map and the octahedral recurrence, are motivated by concrete algebraic constructions (taking determinants) or geometric constructions based on specific configurations of points and lines in the projective plane. The systems of interest in this workshop have connections to Poisson and symplectic geometry, classical integrable PDE such as the KdV and Boussinesq equations and also to cluster algebras. The aim of the workshop is to explore geometric, algebraic, and computational facets of these systems, with a view towards uncovering new phenomena and unifying the work to date.


MondayAugust 25, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
8:30 - 8:55Registration11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:50From friezes to representation theoryPhilippe Caldero, Universite Claude-Bernard (Lyon I)11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20The projective heat mat on pentagonsRich Schwartz, Brown University11th Floor Lecture Hall
11:30 - 12:20The combinatorics of non-commutative discrete integrable systemsPhilippe Di Francesco, Institut de Physique Theorique11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch
2:30 - 3:20Integrability in the Laplacian determinantRichard Kenyon, Brown University11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:50Representation theory and mirror symmetryAlexander Goncharov, Yale University11th Floor Lecture Hall
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5:00 - 6:30Welcome Reception11th Floor Collaborative Space

TuesdayAugust 26, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:50The Devron propertyMax Glick, University of Minnesota11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20The point of collapse under pentagram mapsZijian Yao, Brown University11th Floor Lecture Hall
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11:30 - 12:20Combinatorial Gale transformValentin Ovsienko, Institut Camille Jordan, Université Lyon 111th Floor Lecture Hall
12:30 - 2:30Break for Lunch
2:30 - 3:20Spectral theory of triangular difference operators and the combinatorial Gale transformIgor Krichever, Columbia University11th Floor Lecutre Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:50Characters of graded tensor products, difference equations and $q$-Whittaker functionsRinat Kedem, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
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WednesdayAugust 27, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:50Dented diagonals and corrugated polygonsBoris Khesin, University of Toronto11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20Integrability of pentagram maps and Lax representationsFedor Soloviev, University of Toronto11th Floor Lecture Hall
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11:30 - 12:20What is integrability of (discrete) variational systems?Yuri Suris, Technische Universität Berlin11th Floor Lecture Hall
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12:20 - 12:30Group Photo11th Floor Lecture Hall
12:30 - 2:30Break for Lunch
2:30 - 3:20Discrete pluriharmonic functions as solutions of linear pluri-Lagrangian systemsAlexander Bobenko, Technische Universitat Berlin11th Floor Lecture Hall
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3:30 - 4:20Cluster co-ordinates and some integrable equationsAndrei Marshakov, Lebedev Physics Institute and Institute of Theoretical and Experimental Physics 11th Floor Lecture Hall
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4:30 - 6:30Poster Session and Coffee Break11th Floor Collaborative Space

ThursdayAugust 28, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:50Dimer models and categories with Grassmannian structureKarin Baur, Karl-Franzens-Universitat Graz11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20Subtraction-free complexitySergey Fomin, University of Michigan11th Floor Lecture Hall
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11:30 - 12:20Cluster structure on Drinfeld doublesMichael Gekhtman, University of Notre Dame11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch
2:30 - 3:20TBAVladimir Fock, Université de Strasbourg I (Louis Pasteur)11th Floor Lecture Hall
3:20 - 3:20Please take a moment to complete the survey that was distributed by email.
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:50Brick polytopes and generalized associahedraVincent Pilaud, CNRS & LIX, École Polytechnique11th Floor Lecture Hall
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FridayAugust 29, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:50Exotic cluster structures on SL(N)Michael Shapiro, Michigan State University11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20R-operator and knot invariants via cluster algebraRei Inoue, Chiba University11th Floor Lecture Hall
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11:30 - 12:20Continuous limit of frieze patterns and discretization of a Virasoro orbitSergei Tabachnikov, ICERM and Pennsylvania State University11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch
2:30 - 3:20TBAGregg Musiker, University of Minnesota11th Floor Lecture Hall
3:30 - 4:20TBARalf Schifler, University of Connecticut11th Floor Lecture Hall