401-4162-00L Cluster Algebras
|Semester||Spring Semester 2018|
|Lecturers||R. J. Tessler|
|Language of instruction||English|
|Abstract||The topic of the course is the theory of cluster algebras, introduced by Fomin and Zelevinsky.|
Cluster algebras are a class of commutative rings defined in some combinatorial manner.
They appear naturally in distinct areas of mathematics - total positivity, tropical geometry, Teichmuller theory, Poisson geometry and more.
|Objective||Understand the notion of cluster algebra, know basic tools in the theory and several examples from different areas of mathematics where cluster algebras appear.|
|Content||We shall start with total positivity as a motivating example. |
We then define cluster algebras and classify cluster algebras of finite type.
The next topic is relations with Teichmuller theory.
If time permits - we do more!
|Prerequisites / Notice||Linear algebra. Algebra (basic group theory and familiarity with commutative rings) |
Basic knowledge of Lie theory and root systems.