index

“Mom, can we stop and get some Wikipedia?” Mom: “We have Wikipedia at home” Wikipedia at home:

Introduction

Welcome to my mighty Obsidian Vault! This is a place where I store math articles, lecture notes, conference notes and literature notes. It functions as my primary place to learn and organise concepts in mathematics. Think of a small-scale Wikipedia but more reflective of my own knowledge. This vault has been created around 2022 and slowly but steadily growing. Now it contains around 2000 notes.

The explorer on the left gives a good indication how the vault is organised.

• Klassifikation is the most important section. It contains notes, sorted by their Mathematics Subject Classification Code
• Literatur contains a note for each paper and book I included in the vault. The notes are usually empty but they contain backlinks to the articles talked about in the book
• Projekte contains projects I am currently working on
• Veranstaltungen contains current events and lectures I am currently visiting.

If you are someone who wants to learn more about me or gauge my expertise then below are some highlighted pages you might be interested in.

Conference Notes

I participated in the following conferences. Click on the names to get more details and access my notes made during the talks. I take notes primarily in order to stay awake listen actively to the lecturer. If possible I try to write down true statements.

File	Date	Location	Homepage
Integral Structures in Geometry and Representation Theory	2024/09/09	University Paderborn, Germany	https://trr358.math.uni-bielefeld.de/workshops/view/191
Intelligence of Low-Dimensional Topology 2024	2024/03/22	Kyoto University	https://www.kurims.kyoto-u.ac.jp/~ildt/index-en.html
2023WiSe MSJ Spring Meeting 2024	2024/03/17	Osaka Metropolitan University, Japan	https://www.mathsoc.jp/en/meeting/omu24mar/
The 19th East Asian Conference on Geometric Topology	2024/02/19	Kyoto University, Japan	https://www.kurims.kyoto-u.ac.jp/~eacgt/
Magnitude 2023	2023/12/4	Osaka University, Japan	https://sites.google.com/view/magnitude2023/home
Topology and Computers 2023	2023/10/20	Keio University, Japan	https://sites.google.com/keio.jp/topocom2023
Hensel - Differentiable Manifolds	-	-	-

Current Lectures and Seminar

This lists all of math lectures this semester. Mind that I also have computer science and teaching lectures which are not listed here.

File	Content
4-Dimensional Manifolds 2023	Quasikonforme Fläche, Konferenz Takamura - Higher Group theory and its geometry, Fuchsian group, Idealer Rand (Riemannsche Fläche), Quasikonforme Abbildung, Teichmüller-Metrik, Teichmüller-space, Teichmüller-Äquivalenz, Graduierte Dimension, Graduierte Euler-Charakteristik, Graduierter Vektorraum, Gradverschiebung (Kettenkomplex), Khovanov-Homologie, Henkelkörperdiagramm, Henkelzerlegung, Morsefunktion, Henkelkörper, Konferenz Asano - On lower bounds for the Kirby-Thompson nvarient by using homology groups, Konferenz Ogawa - Shadow Complexity and Trisection Genus, Konferenz Sugawara - Handle decompositions and Kirby diagrams for the complement of plane algebraic curves, Genus Funktion, Konferenz Hamada - Exotic 4-manifolds with signature zero via Lefschetz fibrations, Signatur (Topologie), Limit set
Bauer & Hensel - Aspects and Applications of Representation Theory	Representation of the mapping class group, Torelli Group, Mapping class group, Regular Cover, Characteristic subgroup
Bowden & Hensel - Fuchssche Gruppen	Cycle (Fuchsian group), Dirichlet region, Dirichlet tessellation, Fuchsian group, Modular group, Local finiteness, Limit set
Bowden & Hensel - Geometry and Dynamics of Homeomorphisms in Dimensions 1 and 2	Hyperbolic group, Quasi-isometric embedding, Quasi-geodesic, Quasi-Isometry, Cayley-Graph, Stable commutator length, Commutator length, Geodesic arc, Geodesic, Fellow traveller quasi-axes, Hyperbolic group element, Hyperbolic metric space, Ideal boundary (Hyperbolic groups), Ideal boundary (Hyperbolic space), Morse lemma, Nonelementary action, Quasi-axis, Axial isometry, Weak proper discontinuity, Coarse quasi-homomorphism space, Counting quasimorphism, Generalised counting quasimorphism, Discrete group, Homogeneous quasi-homomorphism space, Quasimorphism
Gerkmann - Algebra und Zahlentheorie (Tutor)	Zentralisator, Zentralisator, Repräsentantensystem (Orbit), Representatives (Orbit), Orbit (Gruppenoperation), Orbit (Group action), Bahngleichung, Gruppenoperation, Group action, Monoid, Halbgruppe, Normalreihe, Kommutatorgruppe, Kommutator, Abelsche Normalreihe, Untergruppe, Subgroup, p-Sylowgruppe, p-Subgroup, Normalisator (Gruppe), Normal subgroup, Konjugationsklasse, Ordnung (Gruppe), Exponent (Gruppe), Einfache Gruppe, Diedergruppe, Alternierende Gruppe, Klassifikation von Gruppen (Elementare Gruppentheorie), Symmetrische Gruppe, Endliche Gruppe, P-Gruppe, Satz von Lagrange, Torsionsuntergruppe, Klein 4-Gruppe, Endliche Abelsche Gruppe, Endlich Erzeugte Gruppe, Zyklische Gruppe, Unendliche Zyklische Gruppe, Endliche Zyklische Gruppe, Hauptsatz über endlich erzeugte Abelsche Gruppe, Endlich Erzeugte Abelsche Gruppe, Abelsche Gruppe, Verknüpfung auf Nebenklassen (Gruppe), Repräsentantensystem (Gruppe), Quotientengruppe, Nebenklasse, Kanonischer Epimorphismus (Gruppe), Homomorphiesatz für Gruppen, Komplexprodukt, Äußeres Direktes Produkt (Gruppe), Inneres Direktes Produkt (Gruppe), Erzeugendensystem, Induzierter Homomorphismus (Faktorgruppe), Kern, Gruppenisomorphismus, Gruppenhomomorphismus, Group homomorphism, Gruppe, Group, Erklärung zu Gruppen, Kategorie, Isomorphismus, Homomorphismus, Größter Gemeinsamer Teiler, Divisor, Zero divisor, Unit, Einheitengruppe, Irreduzibles Element, Prime element, Subring, Ring extension, Generated subring, Extension ring, Repräsentantensystem (Nebenklassen von Ringen), Nebenklasse (Ring), Faktorring, Two-sided Principal ideal, Principal Ideal Domain, Two-sided Ideal, Left ideal, Prime ideal, Maximal ideal, Generated Ideal, Coprime ideals, Direktes Produkt (Ring), Ring homomorphism, Kern (Ring), Homomophiesatz für Ringe, Commutative Ring, Symmetrisches Polynom, Präsentation Symmetrisches Polynom, Hauptsatz von symmetrischen Polynomen, Elementarsymmetrisches Polynom, Primitive Einheitswurzel, Potenzenzykel, Kreisteilungspolynom, Faktorisierung von Kreisteilungspolynomen in endlichen Körpern, Einheitswurzel, Vorlesung über Irreduzibiltätskriterien
Gerkmann - Stexkurs Algebra	Sylow theorems
Hensel - Riemannsche Geometrie
Illustrating Math
Oberseminar Kotschick
Zenk - Stexkurs Analysis	Satz von Fubini, Improper integral, Total derivative, Lagrange multiplier, Directional derivative, Differentiable function, Gradient, Pointwise convergence, Uniform convergence, Hessian, Continuous function, Definite form, Transformationssatz

Currently relevant books and papers

Literature	Author	Content
4-Manifolds	Selman Akbulut	Henkelzerlegung, Morsefunktion, Henkelkörper
Ordinary Differential Equations	Vladimir I. Arnold	Homomorphismus, Group, Gruppe, Abelsche Gruppe, Group action, Gruppenoperation, Orbit (Group action), Orbit (Gruppenoperation)
On Khovanov’s categorification of the Jones polynomial	Dror Bar-Natan	Graduierte Euler-Charakteristik
Bounded cohomology of subgroups of mapping class groups	Mladen Bestvina, Koji Fujiwara	Quasi-Isometry, Quasi-geodesic, Quasi-isometric embedding, Geodesic arc, Geodesic, Fellow traveller quasi-axes, Hyperbolic metric space, Morse lemma, Nonelementary action, Quasi-axis, Axial isometry, Coarse quasi-homomorphism space, Discrete group, Homogeneous quasi-homomorphism space, Quasimorphism, Mathematikartikel - Homeomorphisms of the Circle
Vorbereitungskurs Staatsexamen Mathematik	Dominik Bullach, Johannes Funk	Quotient Rings, Coprime Numbers, Gradient, Chinese Remainder Theorem, Centre (Gruppe), Group action, Orbit (Group action), Differentiable function, Directional derivative, Lagrange multiplier, Total derivative, Satz von Fubini, Pointwise convergence, Uniform convergence, Hessian, Continuous function, Definite form, Transformationssatz
Scl	Danny Calegari	Commutator length, Stable commutator length, Cayley-Graph, Hyperbolic group, Hyperbolic group element, Hyperbolic metric space, Ideal boundary (Hyperbolic groups), Ideal boundary (Hyperbolic space), Weak proper discontinuity, Coarse quasi-homomorphism space, Counting quasimorphism, Generalised counting quasimorphism, Quasimorphism
Visual Group Theory	Nathan Carter	Group, Gruppe, Group homomorphism, Gruppenhomomorphismus, Abelsche Gruppe, Zyklische Gruppe, Klein 4-Gruppe, P-Gruppe, Symmetrische Gruppe, Diedergruppe, Konjugationsklasse, Normalisator (Gruppe), Sylow theorems, p-Subgroup, Cayley-Graph, Group action, Gruppenoperation, Conjugation (subgroup), Orbit (Group action)
Office Hours with a Geometric Group Theorist	Matt Clay, Dan Margalit	Cayley-Graph, Quasi-Isometry, Quasi-isometric embedding
Trisecting 4–Manifolds	David Gay, Robion Kirby	Henkelkörper
Field Theory and Its Classical Problems	Charles Robert Hadlock	Dritteln eines Winkels, Verdoppeln des Würfels, Würfeln eines Kreises
Teichmüller Theory and Applications to Geometry, Topology, and Dynamics	John Hamal Hubbard	Fuchsian group, Limit set
Fuchsian Groups	Svetlana Katok	Cycle (Fuchsian group), Dirichlet region, Dirichlet tessellation, Fuchsian group, Modular group, Limit set, Local finiteness
Asymptotic linearity of the mapping class group and a homological version of the Nielsen-Thurston classification	Thomas Koberda	Characteristic subgroup, Regular Cover, Representation of the mapping class group, Torelli Group, Mapping class group, Mathematikartikel - Representation Theory
Finite Fields for Computer Scientists and Engineers	Robert J. McEliece	Größter Gemeinsamer Teiler
Visual Complex Analysis	Tristan Needham	Gradient
Non-euclidean geometry, continued fractions, and ergodic theory	Caroline Series	Fuchsian group, Limit set
Braids and Dynamics	Jean-Luc Thiffeault	Mapping class group

I love the dynamic dataviews. They are fantastic! The results above are somewhat erratic when I do major changes to the site. Please take them with a grain of salt. Also the recent changes probably only work if I upload regularly.