Welcome to My Website

Please find attached a method to visualize finite groups:

Here we use the exp function to visualize each element of the finite group:

Here we use the exp function to visualize each element of the finite group where each group is in a printable pdf file:

If you are interested in Galois-Theory, here you can find my diploma, where I compute the Galois groups of some polynomials.

If you are interested in some unfinished ideas, I try to collect those in a notebook.

I am mostly interested in positive definite kernels for structured data, especially over the natural numbers and applications thereof (in measuring the consonance of two musical notes and in generating an infinite number of formulas for the circle number pi).

In Some inequalities which are equivalent to the Riemann hypothesis I prove that there exists an infinite number of inequalities similar to the Lagarias inequality, which are equivalent to the Riemann hypothesis.

In Railway networks with Timetables an abstract mathematical model of a railway network with timetables is suggested.

I presented a fast algorithm for the problem "inverse shortest paths in directed acyclic graphs" at the conference KLAIM 2023 in Kaiserslautern with source-code as a Jupyter-Notebook in Python.

In The Mason-Stothers theorem for natural numbers a proof based on the proof by Serge Lang in "Algebra" is given for natural numbers.

Please find attached an image of a fractal I stumbled upon which is based on lexicographic sorting of the prime factorization.

In my spare time I did some algorithmic composition as a hobby, culminating in a participation on the AI song contest 2023.

The method I used to generate this piece for piano, is a combination of Long Short-Term Memory method combined with the positive definite kernel I stumbled upon to measure musical note consonance. The code can be found here.