Paul Breiding

Paul Breiding is a Professor for Mathematical Methods in Data Science at the University of Osnabrück, within the Faculty of Mathematics/Computer Science/Physics. He is part of the Applied Algebra and Data Analysis working group and the Research Unit Data Science. His research focuses on nonlinear algebra, metric algebraic geometry, and their applications in numerical methods and data science.

He is a Fellow of the Junge Akademie Mainz and co-authored the book 'Metric Algebraic Geometry' with Kathlen Kohn and Bernd Sturmfels. His work includes developing the software HomotopyContinuation.jl (v.2.11), which is widely used for numerical algebraic geometry.

His research interests span algebraic geometry, tensor decompositions, and computational methods. Recent publications investigate geometric properties of algebraic varieties, condition numbers in tensor approximations, and probabilistic aspects of algebraic structures.

Key contributions include studies on the reach of algebraic manifolds, typical ranks of random tensors, and sensitivity analysis in numerical algorithms. His work bridges theoretical algebraic geometry with practical computational tools for data science applications.

• Software: HomotopyContinuation.jl (v.2.11)
• Labs/Teams: Applied Algebra and Data Analysis, Research Unit Data Science