Numerical and probabilistic nonlinear algebra with a view towards applications

• Applicant: Professor Dr. Paul Breiding
• Subject Area: Mathematics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 445466444

The aim of this proposal is to develop and establish probabilistic and numerical methods for problems in nonlinear algebra. Specifically, problems from the following areas: computer vision, numerical decomposition of tensors, polynomial equation solving, random algebraic geometry, and sampling from algebraic varieties. The focus lies both on the theoretical foundations and on applications in learning, data science and engineering.The proposed research program lies at the interface of algebraic geometry, numerical analysis and probability theory on the one side, and applied problems from learning, data science and engineering on the other side. It will improve our understanding and our abilities of applying numerical and probabilistic methods in those fields.

• DFG Programme: Independent Junior Research Groups