Paul Breiding is a postdoc in the Nonlinear Algebra group at MPI MiS. He completed his PhD at TU Berlin in 2017 under the supervision of Peter Bürgisser.
His research interests involve geometric probability, numerical analysis, data science, and complexity analysis. He is interested in how algebraic structures can be exploited in those ﬁelds. A signiﬁcant part of his work revolves around tensors. For instance, in a recent article with Carlos Beltrán and Nick Vannieuwenhoven, they proved that a popular class of algorithms for computing tensor rank decompositions is numerically unstable.
Together with Sascha Timme, Paul is developing the software package HomotopyContinuation.jl for numerically computing solutions to systems of polynomials. He is regularly updating a dedicated blog, where he writes posts on how the software is used in research.
July 25, 2018