Dualities in the representation theory and geometry of loop groups

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Representation theory is the study of symmetries appearing in mathematics, physics or in any other natural science. Its main objective is to give an a priori description of data that can appear in a system that exhibits a given symmetry. For „classical" symmetries (finite groups, compact Lie groups, etc.) a large amount of such data is known today. In recent years various new classes of symmetries appeared in the context of infinite dimensional loop groups. Quite surprisingly, significant interrelations between these structures and other areas of mathematics were found. The recurrent appearance of “dualities” belongs to the deepest mysteries in today's mathematics. The project intends to study these dualities by combining two approaches towards the representation theory of loop groups and related structures such as modular or quantum representations.