WiSe 19/20: Computational Algebraic Geometry
Christian Haase
Comments
This course will cover the basics of computational algebraic geometry, including the core algorithms in the subject, as well as introduce some of the most common algebraic varieties which occur in applications. We will gain familiarity with software for algebraic geometry, including the systems Macaulay 2, Singular, Bertini, and PHCpack. Students will complete a final project in the subject which will be presented to the class in lieu of a final exam. Grading will be based on final projects and some written/computer work through the term.
Expected topics to cover:
- Algebraic-geometric dictionary
- Resultants and elimination
- Gröbner bases, including algorithms based on Groebner bases
- Solving polynomial systems symbolically
- Solving systems of polynomial equations using numerical continuation
- Certification of numerical solutions. Smale's α-theory
- Numerical algebraic geometry. Witness sets and numerical irreducible decomposition
- Real root counting. Sturm's theorem. Fewnomial theory
- Toric ideals
- Toric degenerations and Khovanskii bases
21 Class schedule
Additional appointments
Tue, 2020-03-17 10:00 - 16:00
Location:
A6/SR 032 Seminarraum (Arnimallee 6)
Location:
A6/SR 032 Seminarraum (Arnimallee 6)
Regular appointments
Location:
A6/SR 032 Seminarraum (Arnimallee 6)
Location:
A6/SR 032 Seminarraum (Arnimallee 6)
Location:
A6/SR 032 Seminarraum (Arnimallee 6)
Location:
A6/SR 032 Seminarraum (Arnimallee 6)
Location:
A6/SR 032 Seminarraum (Arnimallee 6)