Course Announcement - Summer 2018
Ringvorlesung IMPRS Leipzig

Introduction to Nonlinear Algebra

Instructors:   Bernd Sturmfels   and   Mateusz Michalek

Lectures: Tuesdays, 10:00-12:00, in E1 05
Exercises: Tuesdays, 13:30-15:00, in G3 01

First Day of Lecture: Tuesday, April 10, 2018
Last Day of Lecture: Tuesday, July 10, 2018

Prerequisites: Mastery of Linear Algebra, Basics of Abstract Algebra, No Fear of Computing.

Description: 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: TBD.

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)