Abstract:
This project lies at the interface of representation theory, symplectic geometry and mathematical physics. The main thrust of the project is based on the idea that instead of classifying associative algebras according to their representation type, they can be classified in geometric or physical terms in that they play an important role in geometry or mathematical physics or not. For example, an associative algebra either gives rise to an object in symplectic geometry such as a ((partially) wrapped) Fukaya category or not. The geometric or physical origin of those associative algebras that arise either in the context of symplectic geometry or which are at the origin of physical phenomena, opens a way to understand on the one hand the symplectic geometry or physics and on the other hand the representation theory of these algebras through an interplay of the geometric, physical and algebraic perspectives.