IMPRS Ringvorlesung: Summer semester 2018
- Bernd Sturmfels
- Mateusz Michałek
Abstract
About this lecture
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 scientific members of the IMPRS who introduce different approaches and visions within this field.
Topics
Speakers in this course are: Bernd Sturmfels (BS) and Mateusz Michałek (MM)
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)
- 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)
Date and time info
Tuesdays 10:00 - 12:00
Audience
MSc students, PhD students, Postdocs
Language
English
Links
- B. Sturmfels I, Video (1080p)
- B. Sturmfels I, Video (720p)
- M. Michałek I, Video (1080p)
- M. Michałek I, Video (720p)
- B. Sturmfels II, Video (1080p)
- B. Sturmfels II, Video (720p)
- M. Michałek II, Video (1080p)
- M. Michałek II, Video (720p)
- B. Sturmfels III, Video (1080p)
- B. Sturmfels III, Video (720p)
- B. Sturmfels IV, Video (1080p)
- B. Sturmfels IV, Video (720p)
- M. Michałek III, Video (1080p)
- M. Michałek III, Video (720p)
- B. Sturmfels V, Video (1080p)
- B. Sturmfels V, Video (720p)
- M. Michałek IV, Video (1080p)
- M. Michałek IV, Video (720p)
- B. Sturmfels VI, Video (1080p)
- B. Sturmfels VI, Video (720p)
- B. Sturmfels VII, Video (1080p)
- B. Sturmfels VII, Video (720p)
- M. Michałek V, Video (1080p)
- M. Michałek V, Video (720p)
- M. Michałek VI, Video (1080p)
- M. Michałek VI, Video (720p)
- Slides
