Cluster Algebras and Statistical Physics (August 15-19, 2011)


Organizing Committee

Cluster algebra

 

[Image courtesy David Wilson]

 

 

[Image courtesy of David Thurston]

 

 

[Image courtesy of Richard Kenyon]

 

Description

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, Teichmüller 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.

Download Abstracts Here


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