Geometry and representations of classical and quantum Lie supergroups

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The physical notion of supersymmetry is a unifying principle which ensures that bosonic and fermionic particles in quantum physics obey the same fundamental laws. It has permeated the forefront of mathematical research since 1980s, leading to the creation of some of the deepest theories in diverse areas. The mathematical foundation of supersymmetry lies in the theory of Lie supergroups. This project addresses major outstanding problems in the geometry and representations of Lie supergroups and their quantum analogues. Results will be important to the quest for a consistent quantum theory of all the four interactions in nature.