Summer Graduate School

Cluster algebras are a class of combinatorially defined rings that provide a unifying structure for phenomena in a variety of algebraic and geometric contexts. A partial list of related areas includes quiver representations, statistical physics, and Teichmuller theory. This summer workshop for graduate students will focus on the combinatorial aspects of cluster algebras, thereby providing a concrete introduction to this rapidly-growing field. Besides providing background on the fundamentals of cluster theory, the summer school will cover complementary topics such as total positivity, the polyhedral geometry of cluster complexes, cluster algebras from surfaces, and connections to statistical physics. No prior knowledge of cluster algebras will be assumed.

The workshop will consist of four mini-courses with accompanying tutorials. Students will also have opportunities for further exploration using computer packages in Java and Sage.

List of Minicourses:

1. Nathan Reading (North Carolina State University)
   "Cluster algebras and Coxeter combinatorics"
2. Lauren Williams (University of California, Berkeley)
   "Total positivity"
3. Gregg Musiker (University of Minnesota)
   "Cluster algebras from surfaces"
4. Ralf Schiffler (University of Connecticut)
   "Cluster algebras and tilting theory"

Bibliography (PDF)

For eligibility and how to apply, see the Summer Graduate Workshop homepage

(software) = http://sage.lacim.uqam.ca/)  
(notes) = http://arxiv.org/abs/1102.4844