General Information
Below are the English lectures offered by our group in the summer term 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
- Linear algebraic groups,
- Classical groups,
- Nilpotent and solvable groups,
- Borel subgroups,
- Root systems,
- Classification theorem,
- Structure of semisimple groups.
Contact Time
4 SWS lecture
2 SWS example class
Requirements
Modul "Grundlagen der Mathematik" and “Commutative Algebra”
Lectures "Algebraische Strukturen" and "Einführung: Algebra"
Frequency
The lecture takes place irregularly.
Click here for the KIS entry:
Algebraic Groups (Example Class)
Click here for the OLAT entry:
OLAT
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
- 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
- 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
- regular sequences, Rees' theorem,
- grade and depth, description using Ext, Koszul complex,
- projective dimension, Auslander-Buchsbaum formula,
- dual module, torsionfree and reflexive modules,
- Fitting ideals, Buchsbaum-Eisenbud acyclicity criterion, Hilbert-Burch theorem,
- Cohen-Macaulay rings and modules.
Contact Time
2 SWS lecture
Requirements
Moduls "Grundlagen der Mathematik" and “Commutative Algebra”
Lectures “Algebraische Strukturen”
Frequency
The lecture takes place irregularly.
Click here for the KIS entry:
Lecture Depth and Cohen-Macaulay Rings
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