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  • Course Announcement - Summer 2018
    Ringvorlesung IMPRS Leipzig

    Introduction to Nonlinear Algebra

    Instructors:   Bernd Sturmfels   and   Mateusz Michalek

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

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

    Video recordings of our lectures can be found here.

    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: 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)