Due to the rather broad spectrum of topics within the IMPRS, the curriculum consists of a core curriculum to be attended by all students and a variety of more specialized lectures and courses. The heart of our teaching program certainly is the Ringvorlesung. Each semester the Ringvorlesung focuses on one field and is usually delivered by three scientific members of the IMPRS who introduce three different approaches and visions within this field.

IMPRS Ringvorlesung "Introduction to Nonlinear Algebra"

General information

• Time and location course: Tuesdays 10:00 - 12:00, MPI MiS G3 10
• Speakers: Bernd Sturmfels (BS) and Mateusz Michałek (MM)
• Time and location exercises: Tuesdays 13:30 - 15:00, MPI MiS G2 01
• Target audience: MSc students, PhD students, Postdocs
• Videos from all lectures: Every lecture will be recorded and can be viewed later. For more info, streaming and download see the media WWW page at the MPI MIS.
• Prerequisites: Mastery of Linear Algebra, Basics of Abstract Algebra, No Fear of Computing.
• Preparation materials:see personal page of Mateusz Michałek

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

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.

Schedule

• April 10: Polynomials, Ideals, and Gröbner Bases (BS) (exercises)
• April 17: Algebraic Varieties (MM) (exercises)
• April 24: Elimination and Implicitization (BS) (exercises)
• May 8: Linear Spaces and Grassmannians (MM) (exercises)
• May 15: Nullstellensätze (BS) (exercises)
• May 22: Tropical Algebra (BS) (exercises)
• May 29: Toric Varieties (MM) (exercises)
• June 5: Tensors (MM + BS) (exercises)
• June 12: Representation Theory (MM)(exercises)
• June 19: Invariant Theory (BS) (exercises)
• June 26: Semidefinite Programming (BS) (exercises)
• July 3: Primary Decomposition (MM) (exercises)
• July 10: Polytopes and Matroids (MM) (exercises)