Algebraic surgery and enumerative geometry (A12*)

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

The overall goal is to develop a motivic analogue of the theory of surgery for manifolds, allowing a systematic use of degeneration methods, especially in applications to A¹-enum-erative geometry and residual intersection formulas therein. Since a precise definition of motivic surgery is still missing, we will first investigate its computational consequences, in particular in Witt theory. Witt theory is SL-oriented and η-periodic. These are two fundamental properties that often simplify computations. Therefore, we will also study the role of η-periodic and SL-oriented cohomology theories, with a particular focus on η-periodic SL-cobordism.

• 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. Tom Bachmann; Professorin Dr. Sabrina Pauli