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

Hi, I am Luca Leon Happel. I am a Software Engineer and B.Sc in mathematics (algebraic geometry), who works at the Heinrich Heine University, Forschungszentrum Jülich and Universitätsklinikum Düsseldorf.

Automated theorem proving

mathematics
logic
automated theorem proving
lean4
formal verification
\[ \newcommand{\a}{\text{a}} \newcommand{\b}{\text{b}} \newcommand{\f}{\text{f}} \newcommand{\g}{\text{g}} \newcommand{\T}{\mathbb{T}} \]
Feb 21, 2024
Luca Leon Happel

Definition of \TopTwo

\(\ell^2\)-Invariants

mathematics
topology
algebra
group theory
ring theory
measure theory
functional analysis
differential geometry
differential topology
algebraic topology
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
Luca Leon Happel

Surreale Zahlen

Seminar
Surreale Zahlen
abstract algebra
ring theory
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
Luca Leon Happel

Haskell - Angewandter „abstract nonsense“

Seminar
Haskell
programming
Heinrich-Heine Universität
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
Luca Leon Happel

What are „differential forms“

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

 

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

mathematics
algebraic geometry
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…
Mar 1, 2022
Luca Leon Happel

Sheaves in Minecraft

math
algebraic geometry
sheaves
topology
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…
Oct 29, 2021
Luca Leon Happel

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
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
Luca Leon Happel

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
A few minutes ago I stumbled upon this meme on some math and science forum:
Dec 3, 2020
Luca Leon Happel

A new method to calculate dimension

math
fractals
dimension
calculus
geometry
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
Luca Leon Happel

Bildbesucher - First time using JSDoc

JSDoc
JavaScript
game
programming
As you can see in the image above, today I’ve added JSDoc support to my game, BildBesucher. This means that by visiting http://quoteme.github.io/bildbesucher/docs/, you can…
Apr 18, 2020
Luca Leon Happel

Bildbesucher - A simple jump and run game

programming
game
art
javascript
html
css
Recently, I’ve started to develop a game again, finding a bit of a positive side during the current Corona crisis.
Apr 7, 2020
Luca Leon Happel

 

My first program in the AUR

programming
aur
archlinux
Recently I discovered some more of the incredibly useful features of my favorite text-editor Neovim:
Mar 28, 2020
Luca Leon Happel

Glider - A simple boids based video game

javascript
game
boids
Today, while revisiting my old laptop, I rediscovered a project from just over a year and a month ago:
Feb 27, 2020
Luca Leon Happel

 

intersect.mjs und der Sphären/Boxen-Schnitt

javascript
programming
webgl
math
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
Luca Leon Happel
No matching items