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 (Lecture)

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:

Lecture Cryptography

Example Class Cryptography

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