Gromov–Witten theory and orthogonal modular forms (A10*)

• Subject Area: Mathematics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 444845124

The goal of this project is to relate the Gromov–Witten series of K3 and abelian surface fibrations to modular forms for orthogonal groups, which appear naturally in the geometry of moduli spaces of K3 and abelian surfaces. The classical Enriques surface is a basic test case for which we aim to prove general modularity results. On the modular forms side, we intend to study spaces of orthogonal quasimodular forms and regularizations of divergent Borcherds lifts of meromorphic Jacobi forms.

• 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. Georg Oberdieck