Geodesic cycles and modular forms (A08)

• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 444845124

This project studies two classes of geodesic cycles in orthogonal Shimura varieties, special cycles and Kobayashi geodesics. For special cycles we intend to construct extensions to toroidal compactifications that are compatible with rational relations. We shall also prove injectivity results for the geometric theta correspondence of Kudla–Millson. This has applications to the subproject investigating the cones generated by the classes of special cycles. A complementary project uses derivatives of theta functions to construct new examples of Kobayashi geodesics.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 326: Geometry and Arithmetic of Uniformized Structures (GAUS)
• Applicant Institution: Goethe-Universität Frankfurt am Main
• Project Heads: Professor Dr. Jan Hendrik Bruinier; Professor Dr. Martin Möller