### ICERM Semester Program on "Nonlinear Algebra"

*(September 5 – December 7, 2018)*

**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

**Dan Bates**

(Colorado State, Dept of Mathematics)**Sandra Di Rocco**

(Royal Institute of Technology, Stockholm, Dept of Mathematics)**Jonathan Hauenstein**

(Notre Dame, Dept of Applied and Computational Math. and Stat.)**Anton Leykin**

(Georgia Tech)**Frank Sottile**

(Texas A&M, Dept of Mathematics)**Mike Stillman**

(Cornell, Dept of Mathematics)**Cynthia Vinzant**

(North Carolina State, Dept of Mathematics)