# 401-4162-00L Cluster Algebras

Semester | Spring Semester 2018 |

Lecturers | R. J. Tessler |

Periodicity | non-recurring course |

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. |