Singular: Local-to-global Stuctures in Algebraic Geometry and Applications (B05)

• Subject Area: Mathematics
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 286237555

Continuing the work on a massively parallel toolkit for algebraic geometry, we develop a coordination layer for the convenient design of parallel workflows in computer algebra. Based on local-to-global structures arising from charts and modular methods, algorithmic topics in birational geometry, the cone conjecture, and high energy physics are addressed. Extending the OSCAR framework for covered schemes, we consider as guiding applications non-toric subschemes of toric varieties, elliptic fibrations, and destackification. Our algorithmic methods for short IBP systems for Feynman integrals and multivariate partial fraction decompositions will be advanced and complemented by methods for IBP reduction. New connections to integrable systems broaden the applications of our tools.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 195: Symbolic Tools in Mathematics and their Application
• Applicant Institution: Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau
• Project Heads: Professor Dr. Simon Brandhorst, since 1/2021; Dr. Janko Böhm; Professor Dr. Wolfram Decker, from 1/2021 until 12/2024