Organizing Committee
Abstract

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.

Image for "Integrability and Cluster Algebras: Geometry and Combinatorics"
[Image Courtesy of Rich Schwartz, Brown University]

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, August 25, 2014
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:50am EDTFrom friezes to representation theory - Philippe Caldero, Universite Claude-Bernard (Lyon I)11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTThe projective heat mat on pentagons - Rich Schwartz, Brown University11th Floor Lecture Hall 
11:30 - 12:20pm EDTThe combinatorics of non-commutative discrete integrable systems - Philippe Di Francesco, Institut de Physique Theorique11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch  
2:30 - 3:20pm EDTIntegrability in the Laplacian determinant - Richard Kenyon, Brown University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm EDTRepresentation theory and mirror symmetry - Alexander Goncharov, Yale University11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, August 26, 2014
TimeEventLocationMaterials
9:00 - 9:50am EDTThe Devron property - Max Glick, University of Minnesota11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTThe point of collapse under pentagram maps - Zijian Yao, Brown University11th Floor Lecture Hall
11:30 - 12:20pm EDTCombinatorial Gale transform - Valentin Ovsienko, Institut Camille Jordan, Université Lyon 111th Floor Lecture Hall 
12:30 - 2:30pm EDTBreak for Lunch  
2:30 - 3:20pm EDTSpectral theory of triangular difference operators and the combinatorial Gale transform - Igor Krichever, Columbia University11th Floor Lecutre Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm EDTCharacters of graded tensor products, difference equations and $q$-Whittaker functions - Rinat Kedem, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
Wednesday, August 27, 2014
TimeEventLocationMaterials
9:00 - 9:50am EDTDented diagonals and corrugated polygons - Boris Khesin, University of Toronto11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTIntegrability of pentagram maps and Lax representations - Fedor Soloviev, University of Toronto11th Floor Lecture Hall
11:30 - 12:20pm EDTWhat is integrability of (discrete) variational systems? - Yuri Suris, Technische Universität Berlin11th Floor Lecture Hall 
12:20 - 12:30pm EDTGroup Photo11th Floor Lecture Hall 
12:30 - 2:30pm EDTBreak for Lunch  
2:30 - 3:20pm EDTDiscrete pluriharmonic functions as solutions of linear pluri-Lagrangian systems - Alexander Bobenko, Technische Universitat Berlin11th Floor Lecture Hall
3:30 - 4:20pm EDTCluster co-ordinates and some integrable equations - Andrei Marshakov, Lebedev Physics Institute and Institute of Theoretical and Experimental Physics 11th Floor Lecture Hall 
4:30 - 6:30pm EDTPoster Session and Coffee Break11th Floor Collaborative Space 
Thursday, August 28, 2014
TimeEventLocationMaterials
9:00 - 9:50am EDTDimer models and categories with Grassmannian structure - Karin Baur, Karl-Franzens-Universitat Graz11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTSubtraction-free complexity - Sergey Fomin, University of Michigan11th Floor Lecture Hall
11:30 - 12:20pm EDTCluster structure on Drinfeld doubles - Michael Gekhtman, University of Notre Dame11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch  
2:30 - 3:20pm EDTDiscrete Flows on Cluster Integrable Systems - Vladimir Fock, Université de Strasbourg I (Louis Pasteur)11th Floor Lecture Hall 
3:20 - 3:20pm EDTPlease take a moment to complete the survey that was distributed by email.  
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm EDTBrick polytopes and generalized associahedra - Vincent Pilaud, CNRS & LIX, École Polytechnique11th Floor Lecture Hall
Friday, August 29, 2014
TimeEventLocationMaterials
9:00 - 9:50am EDTExotic cluster structures on SL(N) - Michael Shapiro, Michigan State University11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTR-operator and knot invariants via cluster algebra - Rei Inoue, Chiba University11th Floor Lecture Hall
11:30 - 12:20pm EDTContinuous limit of frieze patterns and discretization of a Virasoro orbit - Sergei Tabachnikov, ICERM and Pennsylvania State University11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch  
2:30 - 3:20pm EDTCluster Variables for DP3 Quiver and Aztec Castle - Gregg Musiker, University of Minnesota11th Floor Lecture Hall 
3:30 - 4:20pm EDTOn Cluster Algebras of Unpunctured Surfaces with One Marked Point - Ralf Schiffler, University of Connecticut11th Floor Lecture Hall 

Lecture Videos

On Cluster Algebras of Unpunctured Surfaces with One Marked Point

Ralf Schiffler
University of Connecticut
August 29, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play

Cluster Variables for DP3 Quiver and Aztec Castle

Gregg Musiker
University of Minnesota
August 29, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play

Continuous limit of frieze patterns and discretization of a Virasoro orbit

Sergei Tabachnikov
ICERM and Penn State
August 29, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

R-operator and knot invariants via cluster algebra

Rei Inoue Yamazaki
Chiba University
August 29, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

Exotic cluster structures on SL(N)

Michael Shapiro
Michigan State University
August 29, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

Brick polytopes and generalized associahedra

Vincent Pilaud
Ecole Polytechnique
August 28, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

Discrete Flows on Cluster Integrable Systems

Vladimir Fock
Universite de Strasbourg I (Louis Pasteur)
August 28, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play

Cluster structure on Drinfeld doubles

Michael Gekhtman
University of Notre Dame
August 28, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

Subtraction-free complexity

Sergey Fomin
University of Michigan
August 28, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

Dimer models and categories with Grassmannian structure

Karin Baur
Karl-Franzens-Universität Graz
August 28, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

Cluster co-ordinates and some integrable equations

Andrey Marshakov
Higher School of Economics (National Research University)
August 27, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

Discrete pluriharmonic functions as solutions of linear pluri-Lagrangian systems

Alexander Bobenko
Technische Universität Berlin
August 27, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

What is integrability of (discrete) variational systems

Yuri Suris
Technische Universität Berlin
August 27, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

Integrability of pentagram maps and Lax representations

Fedor Soloviev
University of Toronto
August 27, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

Dented diagonals and corrugated polygons

Boris Khesin
University of Toronto
August 27, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

Spectral theory of triangular difference operators and the combinatorial Gale transform

Igor Krichever
Columbia University
August 26, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

Combinatorial Gale transform

Valentin Ovsienko
Universite de Reims
August 26, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play

The point of collapse under pentagram maps

Zijian Yao
Harvard University
August 26, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

The Devron property

Max Glick
University of Michigan
August 26, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

Representation theory and mirror symmetry

Alexander Goncharov
Yale University
August 25, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

Integrability in the Laplacian determinant

Richard Kenyon
Brown University
August 25, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

The combinatorics of non-commutative discrete integrable systems

Philippe di Francesco
University of Illinois at Urbana-Champaign
August 25, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play     Abstract

The projective heat mat on pentagons

Richard Schwartz
Brown University
August 25, 2014
Integrability and Cluster Algebras: Geometry and Combinatorics
Play