Math 918, Topics in Algebra: Cluster Algebras (Spring 2017)

 
Instructor: Kyungyong Lee (klee24@unl.edu)

Office Hours: by appointment, or feel free to knock.

Course Description:

In this course we will explore cluster algebras and their connections to combinatorics, geometry, topology, representation theory, and string theory. Cluster algebras were discovered by Fomin and Zelevinsky in 2000. Since then, they have been shown to be related to a wide variety of branches of mathematics and mathematical physics. These fundamental objects can be constructed in an elementary manner. No background is required, as we will start from scratch. 
 
Roughly one-third of the lectures will be devoted to combinatorics including graph theory and algebraic combinatorics, and another one-third to geometry/topology including algebraic geometry, hyperbolic geometry, Teichm\"uller theory and knot theory, and the rest to representation theory as well as homological algebra.


Recommended Survey Articles:

Computer Software:


Grading:

There will be no exams, but registered students are expected to attend and hand in the homework assignments. I encourage collaboration on the homework and/or optional research projects.

Tentative Lecture Schedule

Homework Assignments