Luca Happel’s personal website

Hi, I am Luca Leon Happel. I am a computer scientist/mathematician and B.Sc in mathematics, who works at multiple high class universities and hospitals throughout Germany. I earned multiple awards for my works (e.g. in AI, medical software development,…) and secured funding for my project in cancer treatment. Read more about me…

Publications

monti – AI for Patient Monitoring

AI-based clinical monitoring with advanced ML on high‑security patient data

journal

AI

clinical-monitoring

AI‑based monitoring platform developed at University Hospital Düsseldorf, using advanced AI methods on high‑security clinical patient data to detect complications in heart and oncology patients.
10.1093/ehjdh/ztaf004.
Example data
European Heart Journal - Digital Health

Letters of Acknowledgement

High-Severity Security Remediation

Responsible Disclosure: Critical Infrastructure Software

security-research

responsible-disclosure

reverse-engineering

Independent security audit of a mission-critical software suite used in highly regulated and highest-tier security environments. Identified a high-severity vulnerability that, under some conditions, posed a risk to physical safety, public security and high monetary losses. The finding was responsibly disclosed and formally acknowledged by the vendor. Corrective measures have been implemented to secure the ecosystem.

Blog Posts

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

A practical approach to vector embedding databases for businesses

I have worked my (more than) fair share in many different regulated environments. Here are some tipps.

Luca Leon Happel

Applying topological data analysis to 4 years of NixOS usage

I Had to Give Away All My Laptops Days Before a Deadline. Here Is How I Recovered With A Single git clone

A few weeks ago I was forced to hand over every laptop I owned — days before a critical project deadline. Most developers would panic. I ran git clone and was back to work within the hour. Here are the pros and cons of bulletproofing your digital life using rigorous data science.

Luca Leon Happel

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

Visualizations of covering spaces and their applications to geometry and video games

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 \(g \geq 2\).

Luca Leon Happel

The exponential map of lie groups

Or: what \(e^x\) and \(\pi\) actually are all about and some funny connections betwee machine learning, sailing and the stock market

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.

Luca Leon Happel

Bitwarden for Git Commit Signing

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.

Luca Leon Happel

Commutator subgroups, derived series and their geometric interpretation

From cyclic and dihedral groups to the Heisenberg group: how commutator subgroups detect twists in Cayley graphs

Given a group \(G\), the commutator subgroup \([G,G]\) is defined as the subgroup generated by all commutators:

Luca Leon Happel

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

Not finished yet…

Luca Leon Happel

Bachelorarbeit

I already published my masters thesis here on my website. So why don’t I also publish my bachelors thesis?

Luca Leon Happel

Masterarbeit

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…

Luca Leon Happel

Solving elliptic differential equations

Elliptic differential equations are a class of partial differential equations (PDEs) that arise in various fields of science and engineering.

Luca Leon Happel

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

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 :)

Luca Leon Happel

Types in model theory

I did not finish writing this post. Kinda got busy…

Luca Leon Happel

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

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…

Luca Leon Happel

Affine lineare Transformationen als lineare Transformationen auf dem projektiven Raum

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

Luca Leon Happel

Interfaces as List of Propositions

Or: Applying the Howard-Curry correspondence to OOP interfaces using the calculus of constructions

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.

Luca Leon Happel

Automated theorem proving

WARNING: This is a work in progress. I am currently writing this article and it is not finished yet. I will update it regularly and remove this warning once it is finished.

Luca Leon Happel

$Definition of \TopTwo$

\(\ell^2\)-Invariants

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.

Luca Leon Happel

Surreale Zahlen

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…

Luca Leon Happel

Knot theory - peripheral system

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.

Luca Leon Happel

Go2Jasmin

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).

Luca Leon Happel

Haskell - Angewandter „abstract nonsense“

Dieses Semester habe ich einen Kurs in der Heinrich-Heine Universität in Düsseldorf belegt, welcher sich mit verschiedenen Programmiersprachen beschäftigte. Dabei habe ich…

Luca Leon Happel

What are „differential forms“

Currently while visiting the “KoMa” (Konferenz der deutschsprachigen Mathematikfachschaften / conference of German-speaking mathematics students) I got into a lot of…

Luca Leon Happel

Elliptic curves over the field with four elements (not finished)

We define the affine space \(\mathbb{A}^n_k\) over a ground field \(k\) to be the set of all tuples \((x_1, \dots, x_n)\) with elements in \(k\). In the case of \(n=2\) we…

Luca Leon Happel

Sheaves in Minecraft

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…

Luca Leon Happel

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

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

Luca Leon Happel

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

A few minutes ago I stumbled upon this meme on some math and science forum:

Luca Leon Happel

A new method to calculate dimension

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…

Luca Leon Happel

My first program in the AUR

Recently I discovered some more of the incredibly useful features of my favorite text-editor Neovim:

Luca Leon Happel

Glider - A simple boids based video game

Today, while revisiting my old laptop, I rediscovered a project from just over a year and a month ago:

Luca Leon Happel

intersect.mjs und der Sphären/Boxen-Schnitt

Momentan arbeite ich an meiner intersect.mjs Bibliothek, welche dafür da ist Kollisionen und Schnitte von verschiedenen geometrischen Strukturen in \(n\) dimensionen zu…

Luca Leon Happel

WebGLCS

My first online multiplayer 3D game (written from scratch)

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:

Luca Leon Happel

The game for which I got a price in Brazil

Relic Hunters Zero on Android and Steam

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.

Luca Leon Happel

My second competitive programming challenge

super platform land - Game++ - Community Challange #3

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.

Luca Leon Happel

My frist competitive programming challenge

super platform land - Game++ - Community Challange #2

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.

Luca Leon Happel