Positive Geometry

• Applicant: Professor Dr. Rainer Sinn
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 539677510

Positive Geometry is an emerging field that started in particle physics. It first connected to algebraic combinatorics in mathematics (positive Grassmannian and cluster algebras). The goal of this project is to take the next step and introduce methods from real algebraic geometry. A positive geometry is a semi-algebraic subset of a complex algebraic variety that is intrinsically defined by its canonical form (as opposed to extrinsically defined by polynomial equations and inequalities). We explore this novel geometric approach to semi-algebraic sets, for instance for del Pezzo surfaces and their moduli. Furthermore, we will study at amplituherdra and adjoints through the lens of moment methods in detail.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2458: Combinatorial Synergies