Geometric Representation Theory: Interface of Algebra, Geometry and Topology.

The general aim is to study questions related to algebra, geometry and topology related to simple algebraic groups. The project revisits some of the classical papers by Atiyah, Borel, Bott, Hirzebruch, etc. trying to use the modern methods to improve our understanding of the spaces. One particularly promising direction is to investigate tensor products of representations, in view of understanding the already disproved conjecture by Knutson, which suggests that irreducible characters are regularly invertible. The study explores cases of failure and refines these results by introducing the Knutson Index as a measures non-invertibility across various algebraic groups and commutative rings, providing new insights into group structures and suggesting future research directions.