Characteristic Cycles and Representation Theory

• Applicant: Professor Dr. Thomas Krämer
• Subject Area: Mathematics
• Term: from 2019 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 430165651

The project combines classical algebraic geometry with methods from algebraic analysis and topology. Its main goal is to study subvarieties of abelian varieties via the theory of perverse sheaves and D-modules.In this context a central role is played by characteristic cycles on the cotangent bundle, which capture subtle information on singularities and ramification. They relate Gauss maps to the representations of linear algebraic groups arising from the Tannakian formalism. The combination of both viewpoints is likely to find applications in algebraic geometry and improve our understanding of the arising Tannakian groups.

• DFG Programme: Research Grants