Characteristic Cycles and Representation Theory

The project combines algebraic geometry with the theory of D-modules and perverse sheaves. Its main goal is to study subvarieties of abelian varieties via characteristic cycles, conic Lagrangian cycles on the cotangent bundle which encode subtle information about singularities. The Tannakian formalism leads to a relation between such cycles, Gauss maps and the representation theory of linear algebraic groups. The combination of these topics is likely to find applications both in algebraic geometry and in understanding the arising Tannakian groups.

The project combines algebraic geometry with the theory of D-modules and perverse sheaves. Its main goal is to study subvarieties of abelian varieties via characteristic cycles, conic Lagrangian cycles on the cotangent bundle which encode subtle information about singularities. The Tannakian formalism leads to a relation between such cycles, Gauss maps and the representation theory of linear algebraic groups. The combination of these topics is likely to find applications both in algebraic geometry and in understanding the arising Tannakian groups.

Duration of project

Start date: 10/2020

End date: 03/2024

Research Areas