Notes and talks

Most of this is expository: talks I gave in student seminars at the University of Freiburg, the notes I wrote up afterwards, and a few one-page summaries I still use myself. Some of it is in German, which the titles will tell you. Nothing here is a paper; the papers are on arXiv and in my thesis.

One-page summaries

These are the files people actually come for, so they go first.

• Properties of scheme morphisms — one page, a diagram of which properties of a morphism imply which. The post about it explains how to read it.
• Complex analysis theorems — one page, the theorems of a first course in complex analysis and how they depend on each other.
• Agda/Emacs cheat sheet — two pages of agda-mode keybindings. Nothing to do with the rest of this page; it is the most downloaded file on this site.

Talks and write-ups

• Serre's problem on projective modules — 2013, on the Quillen–Suslin theorem.
• Division algebras — 2015, a Basic Notions talk.
• The smash product of CW-spectra — 2013.
• Infinite loop spaces — 2012.
• Introduction to the seminar on BBD — 2012, the six functors.
• Cobordism spectra — 2012.
• On a theorem of Grothendieck — 2012, talk notes on Weil–Deligne representations.
• The software development approach in mathematics — 2014, handout.
• Why and how to use distributed version control — 2015, the handout to Git for mathematics.
• Model categories: modern algebraic topology — 2013, a block seminar.
• Einführungsvortrag: CW-Komplexe — 2013, in German.
• Elementare Einführung in die Sprache der Kategorien — 2009, in German.
• Tensoren — 2009, in German.
• Komplexe Bott-Periodizität — 2010, in German.
• Postnikov-Türme, k-Invarianten und Hindernisse — 2008, in German.
• Zelluläre Approximation von Abbildungen — 2008, in German.
• Erste Čech-Kohomologie und G-Hauptfaserbündel — 2008, in German.
• Derivierte Kategorien I and II — 2009, in German.
• Das Hilbert-Polynom und die Gelfand-Kirillov-Dimension — 2009, in German.
• Direktes Bild und inverses Bild von D-Moduln — 2009, in German.
• Bedingte Entropie and Bayes' Theorem und Kanalkapazität — 2010, in German, from an information theory seminar.
• Dependency formalisation for improved learning processes — 2010, PKM workshop.

Seminars I organised

Each programme is the last version that went out; the talks below it are the ones I gave myself.

• Seminar on Motives, Freiburg 2012/13 — programme, and my talks: overview, pure motives, the standard conjectures.
• Seminar on Rational Homotopy Theory, Freiburg 2013 — programme.
• Seminar on Homogeneous and Symmetric Spaces, Freiburg 2014 — programme.
• Seminar on Mapping Class Groups, Freiburg 2012/13 — homotopy sheaves.

Diploma thesis, 2011

Matsumotos Satz und A¹-Homotopietheorie (in German, 1.1 MB), and its extended abstract in English. The doctoral thesis is at FreiDok.

If you would rather read than download, there is a list of favourite blog posts.