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 courtesy David Wilson

Confirmed Speakers & Participants

Workshop Schedule

Monday, August 15, 2011
TimeEventLocationMaterials
9:00 - 9:25Registration  
9:25 - 9:30Welcome - Jill Pipher, Director, ICERM11th Floor Lecture Hall 
9:30 - 10:20About lattice integrable systems and cluster algebras - Rinat Kedem, UIUC11th Floor Lecture Hall
10:20 - 11:10Coffee Break  
11:10 - 12:00Non-Commutative Integrability, Paths and Quasi-determinants, Towards Non-Commutative Cluster Algebras - Philippe di Francesco, Saclay11th Floor Lecture Hall
12:00 - 2:45Break for Lunch  
2:45 - 3:35On tropical dualities in cluster algebras - Andrei Zelevinsky, Northeastern11th Floor Lecture Hall
3:35 - 4:05Coffee Break  
4:05 - 4:55T-systems, Y-systems, and cluster algebras - Tomoki Nakanishi, Nagoya University11th Floor Lecture Hall
5:00 - 6:30Welcome Reception  
Tuesday, August 16, 2011
TimeEventLocationMaterials
9:30 - 10:20Singularities of the pentagram map - Max Glick, University of Michigan11th Floor Lecture Hall
10:20 - 11:10Coffee Break  
11:10 - 12:00Cluster algebras and discrete integrable systems - Michael Shapiro, Michigan State11th Floor Lecture Hall
12:00 - 1:45Break for Lunch  
1:45 - 2:30Computer software demos  
2:45 - 3:35Integrability and entropy in cluster maps - Andrew N.W. Hone, University of Kent11th Floor Lecture Hall
3:35 - 4:05Coffee Break  
4:05 - 4:55Dimers and clusters - Richard Kenyon, Brown University11th Floor Lecture Hall
Wednesday, August 17, 2011
TimeEventLocationMaterials
9:30 - 10:20A combinatorial description of the totally nonnegative Grassmannian - Kelli Talaska, U.C. Berkeley11th Floor Lecture Hall
10:20 - 11:10Coffee Break  
11:10 - 12:00KP solitons and cluster algebras - Yuji Kodama, Ohio State11th Floor Lecture Hall
12:00 - 12:10Group Photo in Lecture Hall11th Floor Lecture Hall 
Thursday, August 18, 2011
TimeEventLocationMaterials
9:30 - 10:20Quiver mutation and quantum dilogarithm identities - Bernhard Keller, Jussieu11th Floor Lecture Hall
10:20 - 11:10Coffee Break  
11:10 - 12:00Belavin-Drinfeld classification and cluster structures on simple Lie groups - Michael Gekhtman, Notre Dame11th Floor Lecture Hall
12:00 - 2:45Break for Lunch  
2:45 - 3:35Positivity for cluster algebras from surfaces - Ralf Schiffler, University of Connecticut11th Floor Lecture Hall
3:35 - 4:05Coffee Break  
4:05 - 4:55Cluster Algebras of Surfaces II Towards Bases - Gregg Musiker, University of Minnesota11th Floor Lecture Hall
Friday, August 19, 2011
TimeEventLocationMaterials
9:30 - 10:20n-to-1 Graphs, Discrete Unsolvability of the Inverse Problem - James Morrow, University of Washington11th Floor Lecture Hall
10:20 - 11:10Coffee Break  
11:10 - 11:20Survey Distribution. Please return to 11th floor reception desk.  
11:20 - 12:10Dynamics of surface automorphisms and surface cluster algebras - Dylan Thurston, Columbia University11th Floor Lecture Hall 
12:10 - 1:45Break for Lunch  
1:45 - 2:35Flow polytopes and the Kostant partition function - Karola Meszaros, MIT and University of Michigan11th Floor Lecture Hall
2:35 - 2:55Coffee Break  
2:55 - 3:45Explicit expressions for cluster variables - Kyungyong Lee, University of Connecticut11th Floor Lecture Hall