Organizing Committee
Abstract

Cluster algebras are commutative algebras with a distinguished set of generators grouped into overlapping subsets of fixed cardinality; the generators and the relations among them are not given from the outset, but are produced by an iterative process of successive mutations. These algebras were developed to explain the "Laurent phenomenon", in which certain a priori rational functions defined by these mutations turn out to always be Laurent polynomials. Cluster algebras encode a surprisingly widespread range of phenomena in settings as diverse as quiver representations, Teichm├╝ller theory, invariant theory, tropical calculus, Poisson geometry, and polyhedral combinatorics. This workshop will explore the connection between cluster algebras and various topics in statistical physics, including the dimer model on surfaces, integrable systems such as the KP equation, and certain dynamical systems (Y- and Q-systems) which play an important role in the theory of the thermodynamic Bethe Ansatz.

Image courtesy of David Thurston
Image courtesy of Richard Kenyon
Image for "Cluster Algebras and Statistical Physics"
Image courtesy David Wilson

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, August 15, 2011
TimeEventLocationMaterials
9:00 - 9:25am EDTRegistration  
9:25 - 9:30am EDTWelcome - Jill Pipher, Director, ICERM11th Floor Lecture Hall 
9:30 - 10:20am EDTAbout lattice integrable systems and cluster algebras - Rinat Kedem, UIUC11th Floor Lecture Hall
10:20 - 11:10am EDTCoffee Break  
11:10 - 12:00pm EDTNon-Commutative Integrability, Paths and Quasi-determinants, Towards Non-Commutative Cluster Algebras - Philippe di Francesco, Saclay11th Floor Lecture Hall
12:00 - 2:45pm EDTBreak for Lunch  
2:45 - 3:35pm EDTOn tropical dualities in cluster algebras - Andrei Zelevinsky, Northeastern11th Floor Lecture Hall
3:35 - 4:05pm EDTCoffee Break  
4:05 - 4:55pm EDTT-systems, Y-systems, and cluster algebras - Tomoki Nakanishi, Nagoya University11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception  
Tuesday, August 16, 2011
TimeEventLocationMaterials
9:30 - 10:20am EDTSingularities of the pentagram map - Max Glick, University of Michigan11th Floor Lecture Hall
10:20 - 11:10am EDTCoffee Break  
11:10 - 12:00pm EDTCluster algebras and discrete integrable systems - Michael Shapiro, Michigan State11th Floor Lecture Hall
12:00 - 1:45pm EDTBreak for Lunch  
1:45 - 2:30pm EDTComputer software demos  
2:45 - 3:35pm EDTIntegrability and entropy in cluster maps - Andrew N.W. Hone, University of Kent11th Floor Lecture Hall
3:35 - 4:05pm EDTCoffee Break  
4:05 - 4:55pm EDTDimers and clusters - Richard Kenyon, Brown University11th Floor Lecture Hall
Wednesday, August 17, 2011
TimeEventLocationMaterials
9:30 - 10:20am EDTA combinatorial description of the totally nonnegative Grassmannian - Kelli Talaska, U.C. Berkeley11th Floor Lecture Hall
10:20 - 11:10am EDTCoffee Break  
11:10 - 12:00pm EDTKP solitons and cluster algebras - Yuji Kodama, Ohio State11th Floor Lecture Hall
12:00 - 12:10pm EDTGroup Photo in Lecture Hall11th Floor Lecture Hall 
Thursday, August 18, 2011
TimeEventLocationMaterials
9:30 - 10:20am EDTQuiver mutation and quantum dilogarithm identities - Bernhard Keller, Jussieu11th Floor Lecture Hall
10:20 - 11:10am EDTCoffee Break  
11:10 - 12:00pm EDTBelavin-Drinfeld classification and cluster structures on simple Lie groups - Michael Gekhtman, Notre Dame11th Floor Lecture Hall
12:00 - 2:45pm EDTBreak for Lunch  
2:45 - 3:35pm EDTPositivity for cluster algebras from surfaces - Ralf Schiffler, University of Connecticut11th Floor Lecture Hall
3:35 - 4:05pm EDTCoffee Break  
4:05 - 4:55pm EDTCluster Algebras of Surfaces II Towards Bases - Gregg Musiker, University of Minnesota11th Floor Lecture Hall
Friday, August 19, 2011
TimeEventLocationMaterials
9:30 - 10:20am EDTn-to-1 Graphs, Discrete Unsolvability of the Inverse Problem - James Morrow, University of Washington11th Floor Lecture Hall
10:20 - 11:10am EDTCoffee Break  
11:10 - 11:20am EDTSurvey Distribution. Please return to 11th floor reception desk.  
11:20 - 12:10pm EDTDynamics of surface automorphisms and surface cluster algebras - Dylan Thurston, Columbia University11th Floor Lecture Hall 
12:10 - 1:45pm EDTBreak for Lunch  
1:45 - 2:35pm EDTFlow polytopes and the Kostant partition function - Karola Meszaros, MIT and University of Michigan11th Floor Lecture Hall
2:35 - 2:55pm EDTCoffee Break  
2:55 - 3:45pm EDTExplicit expressions for cluster variables - Kyungyong Lee, University of Connecticut11th Floor Lecture Hall