Talks & Slides

2026

Oct Research Talk Upcoming EN

Turi–Plotkin Homology

École normale supérieure de Lyon · 148 slides.

Rules in GSOS format are natural transformations, and their models are bialgebras. For a simple distributive law $λ : Σ B \Rightarrow B Σ$ , the free bialgebra gives a comonad $G = F U$ , and its bar resolution turns every model into a chain complex. Degree zero collects the quantities that transitions preserve. Degree one finds laws that hold in a model but not in the free one, so the homology sees more than behaviour.

Slides Short Version Notes Sources Paper

Oct Note EN

Turi–Plotkin Homology: Notes for the Talk

Notes for the talk at the École normale supérieure de Lyon · 35 pages.

Companion to the Lyon talk. The background runs from free abelian groups through GSOS rules, bialgebras, the bar construction and Smith normal form to comonad homology, with every definition and proof written out. Then the talk, slide by slide: goal, script, details and answers to likely questions.

PDF Talk Sources Paper

Sep Research Talk EN

Persistent Magnitude Homology for Quantitative Equational Theories

Slides for arXiv:2608.21479 · 37 slides.

A stable barcode for the metric meaning of quantitative axioms. Persistent homology comes from the length filtration of $T_{U} A$ , magnitude homology from its associated graded, and a long exact sequence locates the ends of the bars.

Slides Paper

21 Apr Research Talk Invited EN

Universal Coefficient Theorem and Moore–Mayer–Vietoris Sequence for Homology of Ample Groupoids

South Atlantic Noncommutative Geometry Seminar · 110 slides.

Homology of ample groupoids with coefficients, a universal coefficient theorem for discrete coefficients, and a Mayer–Vietoris sequence for clopen saturated covers $U_{1} \cup U_{2} = G_{0}$ , all proved by explicit chain maps.

Slides Sources Paper

30 Mar Note EN

Human-Centered Mathematics

Note · 5 pages.

Mathematics is learned best as sense-making with good feedback. A short synthesis of Pólya, Thurston and research in cognitive science.

PDF

30 Jan Seminar DE

Konstruktion des Jones-Polynoms aus $U_{q} ({sl}_{2})$

Seminar Knoten und Schleifen · 20 pages.

Link diagrams as morphisms of tangle and ribbon categories, and the Jones polynomial from representations of $U_{q} ({sl}_{2})$ .

Handout

2025

23 Jan Seminar DE

Leray–Serre-Spektralsequenz

Seminar zur Spektraltheorie · 23 pages.

Pages $E_{p, q}^{r}$ with differentials $d^{r} : E_{p, q}^{r} \to E_{p - r, q + r - 1}^{r}$ , the Serre spectral sequence of a fibration, and the homology of ${CP}^{\infty}$ .

Handout

2024

29 Oct Seminar DE

Beschränkte Fredholmoperatoren und deren Fredholmindex auf separablen Hilberträumen

Seminar zur Funktionalanalysis · 16 pages.

Fredholm operators and their index $ind T = \dim \ker T - \dim coker T$ , its invariance under compact perturbations, the Calkin algebra, and a Toeplitz example.

Handout

2022

25 Oct Seminar DE

Natürliche Transformationen, Äquivalenzen von Kategorien, darstellbare Funktoren und das Lemma von Yoneda

Seminar Talk · 6 pages.

Natural transformations, equivalences and representable functors, leading up to the Yoneda lemma $Nat (C (c, -), F) ≅ F (c)$ .

Handout Blog post

2021

13 Sep Research Talk EN

Homological Analysis of Sensor Signals from Power Plants

ML4ITS, ECML PKDD 2021 · 48 slides.

Sliding windows turn sensor signals into point clouds on tori, and their Betti curves help to recognise the signals.

Slides Transcript Paper

11 Jan Research Talk EN

Homological Inference of Embedding Dimensions in Neural Networks

IMTA VII, ICPR 2020, Milano · 24 slides.

The Betti numbers of $T^{q} \times R^{p}$ , read off persistence landscapes, bound the width a layer needs.

Slides Transcript Paper Blog post

2020

4 Aug Research Talk EN

Introduction to Persistent Homology

Chair of Computer Science 6 · 44 slides.

Simplicial complexes, Čech and Vietoris–Rips filtrations, and persistence modules.

Slides Seminar

Jul Research Talk EN

Stop Interpolation Topologically

IWCIA 2020, Novi Sad · 57 slides.

Persistence diagrams tell natural-neighbour interpolation when to stop.

Slides Paper Blog post

6 May Seminar EN

Homological Perspective on Data

Chair of Computer Science 6 · 55 slides.

From topological spaces and simplicial complexes to chains, cycles, boundaries and homology.

Slides Blog post Seminar

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