The Department of Mathematics of Vrije Universiteit Amsterdam welcomes applications for a fully-funded, 4-year PhD position in
Algebra: Building bridges between combinatorics and representation theory. In this project you will work on combinatorial and representation theoretic aspects of cluster algebras and/or applications in physics under the supervision of Ilke Canakci.
The theory of cluster algebras is one of the most active research areas due to its varied applications and the intrinsic beauty of the theory. It has deep connections and applications to different disciplines such as representation theory, combinatorics, hyperbolic and symplectic geometry, topology, number theory and string theory. Cluster algebras are combinatorially defined algebras with strong symmetry properties. Much work on cluster algebras has centred around a) combinatorics arising from geometric models associated with cluster algebras and b) representation theory of algebras associated with quivers (i.e. directed graphs) which provides a setting to associate categorical models for cluster algebras. The interaction between these two approaches provided insights in both directions and, in particular, has connections to symplectic geometry and knot theory.The successful candidate will undertake research on combinatorial and representation theoretic aspects of cluster algebras relating them, for instance, to applications arising in physics. However the precise focus of the project will be adapted to the interests and background of the successful candidate. The preferred starting date is
1 September 2020, or a mutually agreed date thereafter.
Your duties
- doing research towards writing a PhD thesis
- teaching tasks (roughly 15% of your time), which typically consist of supervising exercise classes and correcting homework