General Information
Below are the English lectures offered by our group in the summer term 2026.
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
- global fields,
- modules over Dedekind domain,
- valuation and completion,
- integral elements and orders.
Contact Time
4 SWS lecture
2 SWS example class
Requirements
Lectures "Einführung: Algebra" and “Commutative Algebra”
Lecture "Quadratic Number Fields" helpful
Frequency
The lecture takes place irregularly.
Click here for the KIS entry:
Lecture Algebraic Number Theory
Example Class Algebraic Number Theory
Click here for the OLAT entry:
OLAT
Content
- foundations of homological algebra,
- simplicial complexes and simplicial homology,
- singular homology and cohomology,
- manifolds, in particular smooth oriented manifolds,
- differential forms and de Rham cohomology,
- integration on manifolds, generalized Stokes theorem,
- computation and applications of homology and cohomology,
- de Rham theorem and Poincaré duality.
Contact Time
4 SWS lecture
2 SWS example class
Requirements
Module “Grundlagen der Mathematik” and lectures “Algebraic Structures” and "Einführung: Topologie.
Frequency
The lecture is offered irregularly.
Click here for the KIS entry:
Algebraic Topology of Smooth Manifolds (Lecture)
Algebraic Topology of Smooth Manifolds (Example Class)
Hier geht es zum OLAT-Kurs:
Content
- Categories, functors, natural transformations,
- duality, Yoneda lemma,
- universal constructions, products, limits,
- adjoint functors,
- Abelian categories, kernels, co-kernels, exact sequences.
Contact Time
2 SWS lecture
Requirements
Lectures “Algebraische Strukturen”
Lectures “Grundlagen der Matehmatik”
Frequency
The lecture takes place irregularly.
Click here for the KIS entry:
Click here for the OLAT course:
Content
- Maschke's theorem,
- character tables,
- orthogonality relations,
- rationality questions,
- Burnside theorem,
- induced characters,
- Frobenius groups.
Contact Time
2 SWS lecture
1 SWS example class
Requirements
Lectures “Algebraische Strukturen” and “Einführung: Algebra”.
Frequency
The lecture takes place irregularly.
Click here for the KIS entry:
Lecture Character Theory of Finite Groups
Example Class Character Theory of Finite Groups
Click here for the OLAT course:
OLAT
Content
- normal forms and standard bases for ideals and modules,
- Syzygies, free resolutions and the proof of the Buchberger-criterion,
- calculation of the normalization of Noetherian rings,
- calculation of the primary decomposition of ideals,
- Hilbert function,
- Ext and Tor.
Contact Time
4 SWS lecture
2 SWS example class
Requirements
Lectures "Einführung in das symbolische Rechnen" and “Commutative Algebra” helpful
Frequency
The lecture takes place irregularly.
Click here for the KIS entry:
Example Class Computer Algebra
Click here for the OLAT entry:
OLAT
Content
- Symmetric cryptosystems:
- Stream and block ciphers
- Frequency analysis
- Modern ciphers
- Asymmetric cryptosystems:
- Factorization of large numbers, RSA
- Primality tests
- Discrete logarithm, Diffie-Hellman key exchange, ElGamal encryption, hash functions, signature
- Elliptic curve cryptography (ECC)
- Attack on the discrete logarithm problem
- Factorization algorithms (e.g. quadratic sieve, Pollard's ρ, Lenstra)
Contact Time
4 SWS lecture
2 SWS example class
Requirements
Lectures "Einführung: Algebra" and “Elementare Zahlentheory”
Frequency
The lecture takes place every summer term.
Click here for the KIS entry:
Click here for the OLAT entry:
OLAT
Content
- Compulsory Topics:
- Affine and projective spaces, in particular, the projective line and the projective plane,
- Plane algebraic curves over the complex numbers,
- Smooth and singular points,
- Bézout's Theorem for projective plane curves,
- Topological genus of a curve and the genus formula,
- Rational maps between plane curves and the Riemann-Hurwitz formula.
- In addition, a selection of the following topics is covered:
- Polar and Hessian curves,
- Dual curves and Plücker’s formulas,
- Linear systems and divisors on smooth curves,
- Real projective curves,
- Puiseux-parameterizations of plane curve singularities,
- Invariants of plane curve singularities,
- Elliptic curves,
- Further aspects of plane algebraic curves.
Contact Time
2 SWS lecture
1 SWS example class
Requirements
Lectures “Algebraische Strukturen”, “Einführung: Algebra” and “Einführung: Topologie”.
Frequency
The lecture takes place irregularly.
Click here for the KIS entry:
Lecture Plane Algebraic Curves
Example Class Plane Algebraic Curves
Click here for the OLAT course:
OLAT
Content
- structure of imaginary quadratic number fields,
- ideals and ideal class groups,
- Ideals as geometric lattices,
- finiteness of the ideal class group.
Contact Time
2 SWS lecture
1 SWS example class
Requirements
Lectures “Algebraische Strukturen”
Lectures “Einführung: Algebra" and “Elementare Zahlentheorie” helpful.
Frequency
The lecture takes place every summer term.
Click here for the KIS entry:
Lecture Quadratic Number Fields
Example Class Quadratic Number Fields
Click here for the OLAT course:
OLAT