Nonlinear Algebra and Applications
Paul Breiding, T\"urk\"u \"Ozl\"um \c{C}elik, Timothy Duff, Alexander Heaton, Aida Maraj, Anna-Laura Sattelberger, Lorenzo Venturello, O\u{g}uzhan Y\"ur\"uk
TL;DR
This paper reviews how nonlinear algebra techniques are applied across various scientific and engineering fields, highlighting recent developments and inspiring new research questions.
Contribution
It provides a comprehensive overview of nonlinear algebra applications in multiple domains, connecting recent advances to algebraic geometry.
Findings
Applications in polynomial optimization and PDEs
Insights into algebraic statistics and integrable systems
New algorithms inspired by these topics
Abstract
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration spaces of frameworks, biochemical reaction networks, algebraic vision, and tensor decompositions. Conversely, developments on these topics inspire new questions and algorithms for algebraic geometry.
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