ICERM Semester Program on "Nonlinear Algebra"
(September 5 – December 7, 2018)

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Introduction

The theory, algorithms, and software of linear algebra are familiar tools across mathematics, the applied sciences, and engineering. This ubiquity of linear algebra masks a fairly recent growth of nonlinear algebra in mathematics and its applications to other disciplines. The proliferation of nonlinear algebra has been fueled by recent theoretical advances, efficient implementations of core algorithms, and an increased awareness of these tools.

The benefits of this nonlinear theory and its tools are manifold. Pushing computational boundaries has led to the development of new mathematical theories, such as homotopy methods for numerical algebraic geometry, tropical geometry and toric deformations, and sums of squares methods for polynomial optimization. This uncovered many concrete nonlinear mathematical objects and questions, many of which are ripe for computer experimentation. In turn, resulting mathematical breakthroughs often lead to more powerful and efficient algorithms for computation.

This semester will work towards a time when ideas of nonlinear algebra, its theory, methods, and software are as ubiquitous as those of linear algebra.

Semester Program and Research Cluster Organizers