- Post-Quantum Cryptography methods:
- code based methods,
- lattice based methods,
- hash based methods,
- multivariate methods,
- both public key encryption and signatures,
- quantum attacks like Shor or Grover,
- worst case, average case reduction, complexity analysis,
- fully homomorphic encryption schemes.
General Information
Below are the English lectures offered by our group in the winter term 2026/2027.
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
- 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 for finite matrix groups,
- invariants and covariants of algebraic forms,
- invariant theory of binary forms,
- Cayley’s Ω-process,
- Lie algebra actions and the symbolic method,
- Hilbert’s algorithm,
- degree bounds and complexity.
Contact Time
4 SWS lecture
2 SWS example class
Requirements
none
Frequency
The lecture is offered irregularly.
Click here for the KIS entry:
Algorithmic Invariant Theory (Lecture)
Algorithmic Invariant Theory (Example Class)
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
Contact Time
2 SWS lecture
Requirements
Fundamentals of Mathematics and Cryptography
Frequency
The lecture is offered irregularly.
Click here for the KIS entry:
Post-Quantum Cryptography (Lecture)
Click here for the OLAT course: