$$ \newcommand{\N}{\mathbb{N}} \newcommand{\C}{\mathbb{C}} \newcommand{\R}{\mathbb{R}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\ZZ}{\ooalign{Z\cr\hidewidth\kern0.1em\raisebox{-0.5ex}{Z}\hidewidth\cr}} \newcommand{\colim}{\text{colim}} \newcommand{\weaktopo}{\tau_\text{weak}} \newcommand{\strongtopo}{\tau_\text{strong}} \newcommand{\normtopo}{\tau_\text{norm}} \newcommand{\green}[1]{\textcolor{ForestGreen}{#1}} \newcommand{\red}[1]{\textcolor{red}{#1}} \newcommand{\blue}[1]{\textcolor{blue}{#1}} \newcommand{\orange}[1]{\textcolor{orange}{#1}} \newcommand{\tr}{\text{tr}} \newcommand{\id}{\text{id}} \newcommand{\im}{\text{im}\>} \newcommand{\res}{\text{res}} \newcommand{\TopTwo}{\underline{\text{Top}^{(2)}}} \newcommand{\CW}[1]{\underline{#1\text{-CW}}} % specific for this document \newcommand{\cellOne}{\textcolor{green}{1}} \newcommand{\cellTwo}{\textcolor{red}{2}} \newcommand{\cellThree}{\textcolor{brown}{3}} \newcommand{\cellFour}{\textcolor{YellowOrange}{4}} $$

Blog

Universal properties in category theory simply explained

math
category theory
English

We will explain universal properties in category theory in a simple way, using diagrams and logic.

Aug 9, 2026
9 min

Writing Linux Drivers

computer science
Linux
English
I own an Asus Rog Flow X13 with a 04f3:0c6e Elan Microelectronics Corp. ELAN:Fingerprint fingerprint reader, which currently does not work on Linux1.
Jul 15, 2026
4 min

Can the covariance matrix have imaginary eigenvalues?

math
statistics
linear algebra
English

Can the covariance matrix be non-symmetric? Turns out yes, if we consider random variables that take values in a non-commutative ring. How can we construct such a random variable and what is the significance of it?

May 27, 2026
18 min

RAGs: How your company can skip the boring stuff by using computer science

AI
RAG
Kubernetes
Security
DevOps
Vector Databases
English
I have worked my (more than) fair share in many different regulated environments. Here are some tipps.
Mar 9, 2026
7 min

Applying topological data analysis to 4 years of NixOS usage

NixOS
Linux
Haskell
Git
DevOps
Reproducibility
English

A few weeks ago all my laptops stopped working. Just weeks before my masters thesis deadline! NixOS helped my in this situation a lot, as it allowed me to clone the state of my old machine onto a different temporary laptop, continuing my work and finishing my masters just in time. This led me to analyze my NixOS usage over time

Mar 5, 2026
24 min

Bob’s world

Hacking Super Mario 64 using covering spaces (+ hyperbolic geometry)

topology
geometry
visualization
English

We explore covering spaces — spaces that locally look like the “repetitions” of a base space. A key insight is, that we can gain hyperbolic geometry by looking at the universal cover of a surface of genus \(g \geq 2\).

Mar 1, 2026
16 min

Image of a boat sailing on the globe.

The exponential map of lie groups

algebra
geometry
machine learning
English

We wish to understand what \(\exp(x)\) is. We relate compound interest with sailing and along the way find out what \(\pi\) and \(e\) have in common.

Feb 27, 2026
19 min

Bitwarden for Git Commit Signing

cyber security
encryption
git
programming
English

Signing Git commits is a crucial practice for ensuring the authenticity and integrity of your code and the work you have done. It allows you to verify that the commits that were made by you and your team have not been tampered with. In this post, I’ll show you how to use Bitwarden, a popular password manager, to sign your Git commits.

Feb 18, 2026
2 min

Commutator subgroups, derived series and their geometric interpretation

algebra
group theory
English
Given a group \(G\), the commutator subgroup \([G,G]\) is defined as the subgroup generated by all commutators:
Feb 8, 2026
20 min

The \(\ell^2\)-Alexander torsion and the Thurston norm

algebraic topology
3-manifolds
English
Not finished yet…
Feb 7, 2026
10 min

Bachelorarbeit

math
algebra
geometry
Deutsch
I already published my masters thesis here on my website. So why don’t I also publish my bachelors thesis?
Jan 21, 2026
1 min

Masterarbeit

math
algebra
topology
category theory
Deutsch
I am currently writing my masters thesis about the connection between a generalization of the reidemeister-torsion (called \(\ell^2\)-alexander torsion) and the thurston norm…
Jan 21, 2026
7 min

Solving elliptic differential equations

math
algebra
English
Elliptic differential equations are a class of partial differential equations (PDEs) that arise in various fields of science and engineering.
Oct 31, 2025
11 min

Corne + 2 PSP joysticks/dual trackpoint (Rust/RMK)

computer science
compilers
hardware
esp32
keyboard
rust
English

I designed, wired, built, and programmed (completely from scratch, because no software previously supported 2 joysticks) an ergonomic keyboard using some trash PSP parts. This led PCBWAY to sponsor me :)

Oct 30, 2025
1 min

Differentials, 0-forms and 1-forms – Placing (real) analysis on a rigorous footing

mathematics
differential geometry
differential forms
English
I have written about differential form before (What are „differential forms), but there I have never adressed the elephant in the room, of why, we should consider \(df\) as…
Sep 27, 2025
8 min

Affine lineare Transformationen als lineare Transformationen auf dem projektiven Raum

math
algebra
Deutsch

Kurze Notizen, wie man affin-lineare Transformationen auf dem \(\mathbb{R}^n\) als lineare Transformationen auf dem \(\mathbb{R}^{n+1}\) betrachten kann.

Aug 17, 2025
1 min

Onion architecture

Interfaces as List of Propositions

mathematics
category theory
oop
English

This post came to be due to my close friend Stefan Schulz with whom I studied computer science and mathematics at the University of Düsseldorf, after we had a discussion about the way interfaces are used in object-oriented programming languages like Java. It turns out, that we can regard these as a list of propositions, which can be proven by implementing the interface. This is closely related to the Howard-Curry correspondence and some functional programming concepts.

May 31, 2025
6 min

Definition of \TopTwo

\(\ell^2\)-Invariants

mathematics
topology
algebra
group theory
ring theory
measure theory
functional analysis
differential geometry
differential topology
algebraic topology
English

This article is about the \(\ell^2\)-Invariants of \(G\)-CW-complexes. We will start by constructing the \(\ell^2\)-completion of cellular chain complexes and then take a look at some applications of the \(\ell^2\)-completion of cellular chain complexes. We will calculate the \(\ell^2\)-homology groups and the \(\ell^2\)-betti numbers of \(S^\infty := \colim_n S^n\) with the group \(G:=\prod_{n=0}^\infty \Z/2\Z\) acting on it. We will also take a look at the \(\ell^2\)-betti numbers of the torus and the \(\ell^2\)-betti numbers of the universal covering space of the torus. Finally, we will take a look at Lück’s theorem and its implications for the \(\ell^2\)-betti numbers of the universal covering space of a connected, compact CW-complex whose fundamental group is residually finite.

Feb 4, 2024
25 min

Surreale Zahlen

Seminar
Surreale Zahlen
abstract algebra
ring theory
Deutsch
In diesem Vortrag ging es darum zu zeigen, dass die surrealen Zahlen ein Körper sind. Ich arbeitete dabei unter der Annahme, dass wir bereits gezeigt haben, dass \(\boldsymbo…
Nov 16, 2023
1 min

Knot theory - peripheral system

math
algebra
abstract algebra
knot theory
English

In knot theory, the peripheral system is an important concept that helps to classify and distinguish different knots. In this video I animated it for an oberseminar at Heinrich Heine University during my masters degree in mathematics.

May 5, 2023
1 min

Go2Jasmin

computer science
compilers
English

Writing assembly code by hand is tedious and error-prone. Go2Jasmin is a compiler that translates a subset of the Go programming language into Jasmin assembly code for the Java Virtual Machine (JVM). This was a project I did during my bachelor’s degree in computer science for a good grade and for fun. Ultimately I decided to skip my bachelor’s degree in computer science to pursue a PhD in computer science afterwards, so this project was only really for fun (and its good grade never proved useful).

Jan 30, 2023
1 min

Haskell - Angewandter „abstract nonsense“

Seminar
Haskell
programming
Heinrich-Heine Universität
Deutsch
Dieses Semester habe ich einen Kurs in der Heinrich-Heine Universität in Düsseldorf belegt, welcher sich mit verschiedenen Programmiersprachen beschäftigte. Dabei habe ich…
Jan 23, 2023
1 min

What are „differential forms“

mathematics
differential geometry
differential forms
tangent space
cotangent space
manifold
tangent bundle
cotangent bundle
exterior algebra
global section
English
Currently while visiting the “KoMa” (Konferenz der deutschsprachigen Mathematikfachschaften / conference of German-speaking mathematics students) I got into a lot of…
May 27, 2022
2 min

Sheaves in Minecraft

math
algebraic geometry
sheaves
topology
Minecraft
English
A few days ago, after my introductory class in topology, and right before my class about algebraic geometry, my friend Anastasia and I were asked by fellow topology students…
Oct 29, 2021
10 min

Prove that \(\mathbb{R}[x]/(x^2+bx+c)\) is isomorphic to \(\mathbb{R}^2\) or \(\mathbb{C}\) - A proof

math
algebra
abstract algebra
ring theory
meme
English
Around one year ago I tried to solve the following riddle involving abstract algebra, but I failed and did not finish the question at that
Oct 21, 2021
2 min

Rational Points on Elliptic Curves

mathematics
algebraic geometry
English

A presentation I gave in a seminar on elliptic curves, covering the Weierstraß normal form and the group law on elliptic curves.

May 21, 2021
1 min

Prove that \(\mathbb{R}[x]/(x^2+bx+c)\) is isomorphic to \(\mathbb{R}^2\) or \(\mathbb{C}\) - First try

math
algebra
ring theory
abstract algebra
polynomial rings
quotient rings
isomorphisms
English
A few minutes ago I stumbled upon this meme on some math and science forum:
Dec 3, 2020
1 min

A new method to calculate dimension

math
fractals
dimension
calculus
geometry
English
A few days ago, I stumbled upon an article titled Finally We May Have a Path to the Fundamental Theory of Physics… and It’s Beautiful by Stephen Wolfram, an American…
May 22, 2020
5 min
 

My first program in the AUR

programming
linux
English
Recently I discovered some more of the incredibly useful features of my favorite text-editor Neovim:
Mar 28, 2020
3 min

Glider - A simple boids based video game

programming
game
boids
English
Today, while revisiting my old laptop, I rediscovered a project from just over a year and a month ago:
Feb 27, 2020
1 min
 

intersect.mjs und der Sphären/Boxen-Schnitt

javascript
programming
webgl
math
Deutsch
Momentan arbeite ich an meiner intersect.mjs Bibliothek, welche dafür da ist Kollisionen und Schnitte von verschiedenen geometrischen Strukturen in \(n\) dimensionen zu…
Feb 14, 2020
3 min

WebGLCS

computer science
game development
English

I was kinda obsessed with the game Cave Story for a long time. I wanted to expand on it, make it look better (3D, lighting, …) and also be able to play it with my friends online. Remind you, back then in 2015-2027 the software-development landscape was much harsher than today. There were no game engines that would allow you to all that! (At least I did not know of any?). Also, my budget was 0€, so I needed to get creative. This is the result:

Apr 19, 2017
1 min

The game for which I got a price in Brazil

computer science
game development
English

This game was a collaborative effort by a lot of people. I contributed by fixing some minor bugs and (this was kinda unthinkable for a LOT of people back then) porthing this game to Android.

Jan 8, 2015
1 min

Qcoded: the website I built when I was 13

computer science
game dev
nostalgia
English

Back in 2014, at 13 years old, I ran a small German indie game dev website called Qcoded. I built small games in my free time and used the site to host and share them. Here’s a glimpse of what it looked like.

Dec 13, 2014
2 min

My second competitive programming challenge

computer science
game development
English

In this video I showcase my submission for the Game++ Community Challenge #3, my second competitive programming challenge. Back when I was 14, the landscape of game development and competitive programming was quite different from today. Tools and resources were not as readily available, making it a unique experience to participate in such challenges. I was especially proud of integrating the gamepad api into my JavaScript game. This required more “low-level” programming compared to what I was used to previously. In fact, this was (and possibly still is?) kinda unique for web games, as most web games rely on keyboard and mouse inputs.

Jul 15, 2014
1 min

My frist competitive programming challenge

computer science
compilers
English

From a young age I was fascinated by programming video games. Ultimately this culminated in my participation in various competitive programming challenges (and even winning some high ranking university led challenges many years later!). This video shows my first competitive programming challenge, which I participated in when I was only 14 years old.

May 20, 2014
1 min
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