General Information
Below are the English lectures offered by our group in the winter term 2024/2025.
If you would like to attend a seminar or reading course during the winter semester, please contact the respective supervisor by e-mail. Appointments are then determined in consultation with the participants.
If you would like to write a thesis in our working group, simply contact the desired supervisor directly.
Content
Mandatory content:
- Affine and projective varieties (especially: dimension, morphisms, smooth and singular points, blow-ups of points, applications and examples),
- Sheaves and sheaf cohomology with applications (Riemann-Roch's theorem for curves, projective embedding of curves).
It also covers a selection of the following topics:
- Schemes,
- Differential forms,
- other aspects of algebraic geometry.
Contact Time
4 SWS lecture
2 SWS example class
Requirements
Module "Commutative Algebra".
Knowledge from the course "Plane Algebraic Curves" is desirable and helpful, but not necessarily required.
Frequency
The lecture is offered every year in the winter semester.
Click here for the KIS entry:
Algebraic Geometry (Example Class)
Hier geht es zum OLAT-Kurs:
Content
- LLL algorithm,
- Number fields, ring of integers, units, class group,
- Decomposition behavior of primes,
- Algorithmic calculation of these quantities.
Contact Time
4 SWS lecture
2 SWS example class
Requirements
Courses "Algebraic Structures" and "Introduction: Algebra";
In addition, basic properties of Dedekind rings from the course "Commutative Algebra" are used. Knowledge from the "Quadratic Number Fields" module is desirable and helpful.
Frequency
The lecture takes place irregularly.
Click here for the KIS entry:
Vorlesung Algorithmic Number Theory
Übungen Algorithmic Number Theory
Hier geht es zum OLAT-Kurs:
Content
- Rings, modules, localization, lemma of Nakayama,
- Noether / Artin rings and modules,
- Primary decomposition,
- Krull's Principal Ideal Theorem, dimension theory
- Integral ring extensions, going-up, going-down, normalization,
- Noether normalization, Hilbert's Nullstellensatz,
- Dedekind rings, invertible ideals.
Contact Time
4 SWS lecture
2 SWS example class
Requirements
Lecture "Algebraische Strukturen".
The lecture "Introduction: Algebra" is nice to have, but not necessary.
Frequency
The lecture is offered every year in the winter semester.
Click here for the KIS entry:
Commutative Algebra (Example Class)
Click here for the OLAT course:
Content
- Algorithms for computing orbits, transversals, stabilisers; applications thereof,
- Fundamental Algorithms for permutation groups, e.g. stabiliser chains, Schreier-Sims algorithm, backtrack search,
- Algorithms for finitely presented groups, e.g. Tietze transformations, coset enumeration, Abelian invariants, subgroup presentations.
Contact Time
2 SWS lecture
1 SWS example class
Requirements
Modul "Grundlagen der Mathematik"
Lectures "Algebraische Strukturen" and "Einführung: Algebra"
Frequency
The lecture takes place irregularly.
Click here for the KIS entry:
Algorithmic Group Theory (Vorlesung)
Algorithmic Group Theory (Übung)
Click here for the OLAT course: