In recent works, the applicant developed new techniques from combinatorics/graph theory in order to study the representation theory of quantised coordinate rings
, whereas the host has been developing algorithmic methods in order to study the representation theory of these noncommutative algebras.
Among cluster algebras are coordinate rings
of many algebraic varieties that play a prominent rule in representation theory, invariant theory, the study of total positivity, and other areas, but the discussion here is limited to the relations of cluster algebra theory to Poisson geometry and the theory of integrable systems.
The subject of Quantum Groups is a rapidly diversifying field of mathematics and mathematical physics, originally launched by developments in theoretical physics and statistical mechanics involving quantum analogues of Lie algebras and coordinate rings of algebraic groups.
The aim of the course is to provide young researchers with the necessary tools to tackle open problems in the subject area, giving them the opportunity to learn the most recent results on the structure and representation theory of quantized coordinate rings and quantized enveloping algebras.