Lectures: MWF 11:45am-12:40pm in Physics P130.
Instructor: Mikhail Movshev(mmovshev "at" math.sunysb.edu)
Office Hours: MWF TBA Math Tower 4-109. Also, by appointment, or feel free to knock.
This is a graduate level course on
cluster algebras. 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 course will focus on the algebraic,
geometric and combinatorial aspects of cluster algebras, thereby
providing a concrete introduction to this rapidly-growing field.
Besides providing background on the fundamentals of cluster theory,
we will discuss complementary topics such as total positivity, quiver
representations, the polyhedral geometry of cluster complexes,
cluster algebras from surfaces, and connections to statistical
Prerequisites: No prior knowledge of cluster algebras or representation theory will be assumed; although familiarity with groups, rings, and modules will be helpful.
Recommended (but not required) Texts:
Cluster Algebras and Poisson Geometry by Michael Gekhtman, Michael Shapiro, and Alek Vainshtein (2010, AMS Monograph). On reserve in the math library
Elements of the Representation Theory of Associative Algebras, Vol. 1, by Ibarahim Assem, Daniel Simson, and Andrzej Skowronski. (2006, Cambridge University Press) On reserve in the math library
Surveys for Cluster Algebras:
Relevant Research articles
More articles , links to courses and relevant software are available at the Cluster Algebras Portal.
For Quiver Representations and later in the course:
There will be no exams, but registered students are expected to present (orally) solutions of assigned problems (90% of each section) during office hours.The list of problems will be expanded during the course of the semester. Any form of collaboration on homework between students is welcomed.