ICERM

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

Organizing Committee

Lauren Williams
(University of California at Berkeley)
David Wilson
(Microsoft Research)

Images

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

Participant List (* = to be confirmed)

Melody Chan
(University of California, Berkeley)
Philippe di Francesco *
(Commissariat à l'Énergie Atomique Saclay (CEA))
Michael Gekhtman *
(University of Notre Dame)
Max Glick *
(University of Michigan)
Andrew Hone *
(University of Kent at Canterbury)
Theo Johnson-Freyd
(University of California, Berkeley)
Adrien Kassel
(École Nationale Supérieure de Télécommunications (ENST))
Rinat Kedem *
(University of Illinois at Urbana-Champaign)
Bernhard Keller *
(Université de Paris VII (Denis Diderot))
Richard Kenyon *
(Brown University)
Ryan Kinser
(Northeastern University)
Yuji Kodama *
(Ohio State University)
Christian Korff
(University of Glasgow)
Chul-hee Lee
(University of California, Berkeley)
Kyungyong Lee *
(Wayne State University)
Nan Li
(Massachusetts Institute of Technology)
Kenichi Maruno
(University of Texas Pan American)
Karola Meszaros *
(Massachusetts Institute of Technology)
Jim Morrow *
(University of Washington)

Gregg Musiker *
(University of Minnesota)
Tomoki Nakanishi*
(Nagoya University)
James Propp*
(University of Massachusetts)
Pavlo Pylyavskyy
(University of Minnesota)
Steven Sam
(Massachusetts Institute of Technology)
Ralf Schiffler *
(University of Connecticut)
Michael Shapiro *
(Michigan State University)
Linhui Shen
(Yale University)
Salvatore Stella
(Northeastern University)
Nike Sun
(Stanford University)
Kelli Talaska *
(University of California, Berkeley)
Peter Tingley
(Loyola University)
Zhen Wei
(University of Virginia)
Harold Williams
(University of California, Berkeley)
Lauren Williams *
(University of California, Berkeley)
David Wilson *
(Microsoft Research)
Wei Wu
(Brown University)
Andrei Zelevinsky *
(Northeastern University)

Video Archive

Dates	Title	Organizers
August 15-19, 2011	Cluster Algebras and Statistical Physics	Lauren Williams, David Wilson

Video Links
Description	Speaker	Video	Abstract	Slides
A combinatorial description of the totally nonnegative Grassmannian	Kelli Talaska, U.C. Berkeley
Belavin-Drinfeld classification and cluster structures on simple Lie groups	Michael Gekhtman, Notre Dame
KP solitons and cluster algebras	Yuji Kodama, Ohio State
Non-Commutative Integrability, Paths and Quasi-determinants: Towards Non-Commutative Cluster Algebras	Philippe di Francesco, Saclay
On tropical dualities in cluster algebras	Andrei Zelevinsky, Northeastern
n-to-1 Graphs, Discrete Unsolvability of the Inverse Problem	James Morrow, University of Washington

Schedule

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
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
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
10:20 - 11:10	Coffee break
11:10 - 12:00	KP solitons and cluster algebras	Yuji Kodama, Ohio State
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