401-4162-00L  Cluster Algebras

SemesterSpring Semester 2018
LecturersR. J. Tessler
Periodicitynon-recurring course
Language of instructionEnglish

AbstractThe 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.
ObjectiveUnderstand the notion of cluster algebra, know basic tools in the theory and several examples from different areas of mathematics where cluster algebras appear.
ContentWe 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 / NoticeLinear algebra. Algebra (basic group theory and familiarity with commutative rings)
Basic knowledge of Lie theory and root systems.