ICERM Semester Program on "Nonlinear Algebra"
(September 5 – December 7, 2018)
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 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
- Frank Sottile
(Texas A&M, Dept of Mathematics)
- Mike Stillman
(Cornell, Dept of Mathematics)
- Cynthia Vinzant
(North Carolina State, Dept of Mathematics)
Associated Events & Information
Fall 2018 Semester Workshops
|September 5-7 and September 10-12, 2018||Nonlinear Algebra Bootcamp||Dan Bates, Anton Leykin, Mike Stillman|
|September 17-21, 2018||Core computational methods||Wolfram Decker, Jesus de Loera, Andrew Sommese, Mike Stillman|
|October 15-19, 2018||Real algebraic geometry and optimization||Greg Blekherman, Didier Henrion, Pablo Parrilo, Rekha Thomas, Cynthia Vinzant|
|November 12-16, 2018||Nonlinear algebra in applications||Alicia Dickenstein, Elisa Gorla, Yang-Hui He, Caroline Uhler, Jonathan Hauenstein|
This page will show upcoming seminars that will be scheduled by organizers, speakers, and participants of the Fall 2015 semester program. Walk-ins are welcomed and encouraged for these seminars. Please check back regularly for updates.
We provide an iCal link for those attendees who wish to sync their own devices and/or calendars to our schedule.