Inhalt des Dokuments
Schedule
There will be no lectures in the weeks June 4-8 and June 18-22 !!
Replacement dates:
- Tuesday, July 10: 830 - 1000
- Wednesday, July 11: 1600 - 1730
Typ | Tag | Zeitraum | Raum | Lehrperson |
---|---|---|---|---|
Vorlesung | Tuesday | 1015-1145 | MA 316 | Prof. Dr. Peter
Bürgisser [1] |
Vorlesung | Wednesday | 1415-1545 | MA
316 | Prof. Dr. Peter Bürgisser
[2] |
Übung | Friday | 1015-1145 | MA 316 | Kathlén Kohn
[3] |
Content
Invariant
theory is a classical area of mathematics that played a central role
in the development of algebra, even though many of its concrete
and computational results from the 19th century almost fell into
oblivion. Invariant theory got new impetus with Mumford's introduction
of geometric techniques. Recently, it was discovered that
quantitative and algorithmic questions of classical invariant theory
are closely related to fundamental questions of algebraic
complexity theory. This led to surprising progress for computational
questions.
The goal of the lecture is to give an
introduction to invariant theory, and to prepare students to
understand some of the recent work relating complexity and
invariant theory. Students that intend to write a thesis under the
direction of Prof. Bürgisser are expected to attend this
lecture.
The prerequisites of the course are a basic
knowledge in algebraic geometry (e.g., lecture algebraic geometry
I). Some familiarity with concepts of representation theory is
useful, but not necessary.
Table of Content
[5]
Keywords
- Symbolic Method (Polarization)
- Cayley's Omega Process
- Fundamental Theorem of Invariant Theory
- Reductive groups
- Quotients
- Hilbert-Mumford criterion
- Invariants of finite groups
- Invariants of GL(V)
Literature
- Derksen and Kemper, Computational Invariant Theory, Springer
- Dieudonne and Carrel, Invariant Theory, Old and New, Academic Press
- Dolgachev, Lectures on Invariant Theory, Cambridge Univ. Press
- Hoskins, Geometric Invariant Theory and Syplectic Quotients, lectures notes FU Berlin
- Kraft, Geometrische Methoden in der Invariantentheorie, Vieweg
- Mumford, Fogarty, Kirwan, Geometric Invariant Theory, Springer
- Newstead, Introduction to Moduli Problems and Orbit Spaces, lecture notes, TIFR
- Procesi, Lie Groups: An Approach through Invariants and Representations, Springer
- Sturmfels, Algorithms in Invariant Theory, Springer
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s/invariantTheory/zettel-01.pdf
s/invariantTheory/content.pdf