The theory, algorithms, and software of linear algebra are familiar tools across mathematics, the applied sciences, and engineering. This ubiquity of linear algebra masks the fairly recent growth of nonlinear algebra in mathematics and its application. The proliferation of nonlinear methods, notably for systems of multivariate polynomial equations, has been fueled by recent theoretical advances, efficient software, and an increased awareness of these tools. This connects to numerous branches in the mathematical sciences.
The Nonlinear algebra group at MPI Leipzig works on fundamental problems in algebra, geometry and combinatorics that are relevant for nonlinear models. This involves algebraic geometry (complex and real), commutative algebra, combinatorics, polyhedral geometry, and more. On the applications side, we are especially interested in statistics, optimization and the life sciences.
Fields of research are defined by the people who participate. This collection introduces Nonlinear Algebra, an emerging ﬁeld that straddles pure and applied mathematics, by introducing some of its participants. The collection is a snapshot in time, compiled masterfully by Özde Bayer during summer months of 2017 and 2018.
The setting is the Nonlinear Algebra group at the Max-Planck Institute for Mathematics in the Sciences (MPI MiS) in Leipzig, Germany. Our research group started in February 2017, and it has rapidly become an exciting center of activity for a diverse group of mathematicians.
The portraits feature members and visitors of the group in the period between May 2017 and August 2018. Seventy-six "Nonlinear Algebra People" are presented. A brief text introduces each person, their scholarly interests, and their connection to MPI MiS. The date refers to the day when the picture and text ﬁrst appeared online.
I hope you will enjoy this collection.
See you soon at MPI Leipzig!