This course offers an introduction to the concepts
and techniques of Nonlinear Algebra. This
subject covers tools for Mathematics in the Sciences that go beyond the familiar repertoire of Linear Algebra.
The scope is aligned with the MPI group and the ICERM research semester that carry the same name.
Format: The course consists of 13 lectures.
While there is a natural progression of topics, each lecture is
self-contained and independent of the others. Notes will be posted. These include exercises. Informal afternoon
sessions are dedicated to these exercises. Participants with different backgrounds are strongly encouraged to
form study groups and to collaborate. Guests are most welcome to join in on individual Tuesdays.
Grading: Enrolled participants are expected to solve and hand in two or more of the exercises that are listed
after each lecture. The hard deadline for all submissions is Tuesday afternoon in the following week.
April 10: Polynomials, Ideals, and Gröbner Bases (BS)
April 17: Algebraic Varieties (MM)
April 24: Elimination and Implicitization (BS)
May 8: Linear Spaces and Grassmannians (MM)
May 15: Nullstellensätze (BS)
May 22: Tropical Algebra (BS)
May 29: Toric Varieties (MM)
June 5: Tensors (MM+BS)
June 12: Representation Theory (MM)
June 19: Invariant Theory (BS)
June 26: Semidefinite Programming (BS)
July 3: Primary Decomposition (MM)
July 10: Polytopes and Matroids (MM)