Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-44-11-K-7

Algorithmic Invariant Theory (2V+1U, 4.5 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 4.5 CP 93 h
2 V Lecture 28 h
1 U Exercise class (in small groups) 14 h
(2V+1U) 4.5 CP 42 h 93 h

Basedata

SWS 2V+1U
CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Additional informations
Livecycle-State [NORM] Active

Contents

  • definition and basic properties of invariant rings,
  • Reynolds operators, Hilbert series, syzygies,
  • the Cohen-Macaulay property of invariant rings
  • algorithmic methods for computing invariants,
  • Hilbert's finiteness theorem,
  • first fundamental theorem of invariant theory.

Literature

  • B. Sturmfels: Algorithms in Invariant Theory,
  • H. Derksen, G. Kemper: Computational Invariant Theory.

Materials

Further literature will be announced in the lecture(s); exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance (informal)

Knowledge from the course [MAT-41-11-K-7] Computer Algebra is desirable and helpful, but not necessarily required.

Modules:

Courses

Requirements for attendance (formal)

None

References to Course [MAT-44-11-K-7]

Module Name Context
[MAT-44-11-M-7] Algorithmic Invariant Theory P: Obligatory 2V+1U, 4.5 LP