Hey, my name is Lukas. I am a PhD student of mathematics under the supervision of Markus Banagl at Heidelberg University.
Welcome to my website!

About Me

Currently I am working on my PhD thesis on stratified homotopy theory at Heidelberg University. When I don't do mathematics, I'm an avid cook, traveller and boardgame geek.

Academic Interests

Very broadly speaking, I am interested in anything that happens at the intersection of topology and geometry with algebra and category theory. Besides the obvious candidates (Algebraic Topology and Algebraic Geometry) this also includes topological data analysis and the topology of stratified spaces. More specifically I am currently working on my PhD thesis on stratified homotopy theory under the supervision of Markus Banagl. Find a link to some of my past and current projects below.


Over the last few years, I've worked as a teaching assistent for several courses.


Below is a list some past and current projects.

Topic Coauthors Links
Presenting the topological stratified homotopy hypothesis - arXiv
Combinatorial models for stratified homotopy theory - arXiv
On the homotopy links of stratified cell complexes - arXiv
From Samples to Persistent Stratified Homotopy Types (to appear in Proceedings of the 10th ATMCS - Journal of Applied and Computational Topology) Tim Mäder arXiv
From homotopy links to stratified homotopy theories (to appear in Mémoires de la SFM) Sylvain Douteau arXiv
Abelian categories of finitely encodable multiparameter persistence modules (Formely 'Notes on Multiparameter Persistence Modules and Amplitudes') - Version 10.23.23;
A property of the interleaving distance for sheaves Francois Petit, Pierre Schapira arXiv
Amplitudes on abelian categories Barbara Giunti, John S. Nolan, Nina Otter arXiv
Master Thesis: Stratified Homotopy Theory and a Whitehead Group for Stratified Spaces - arXiv


Below is a list of past and upcoming (academic) travel.


When What Where
March 21, 2024 Invited speaker for Journées de topologie algébrique, géométrique et quantique en Picardie Université de Picardie Jules Verne
March 7, 2024 Invited speaker at the Après-midi de Topologie Université Sorbonne Paris Nord


October 17, 2023 Speaker at the EPFL Topology Seminar on my work on pure an applied stratified homotopy theory EPFL Lausanne
September 18 - 22, 2023 Speaker at the Conference on Characteristic Classes and Singular Spaces on my work on a tractable version of the stratified homotopy hypothesis Kiel University
September 7 - 16, 2023 Research visit at the Institut de Recherche en Informatique Fondamentale Institut de Recherche en Informatique Fondamentale, Paris
August 20 - 25, 2022 Poster presentations on "From Samples to Persistent Stratified Homotopy Types" at the ICIAM 2023 Waseda University, Tokyo
July 24 - 28, 2023 Poster presentation on my work on a tractable version of the stratified homotopy hypothesis at the "Young Topologists Meeting 2023" EPFL Lausanne
June 5 - 9, 2023 I attended the conference "A Panorama of Homotopy Theory" University of Oxford
June 19 - 24, 2022 Poster presentations on "Amplitudes on abelian categories" and "From Samples to Persistent Stratified Homotopy Types" at the ATMCS 10 University of Oxford
When What Where
June 13 - 17, 2022 Research Visit and Speaker at the Topology Seminar of Matematiska institutionen, Stockholm University: (Matematiska institutionen, Stockholm University)
August 16 - 20, 2021 I was a (spontaneous substitute) speaker at the SIAM: Conference on Applied Algebraic Geometry. (Virtual)
July 19 - 10, 2021 I attended the Workshop Metrics in Multyparameter Persistence. Lorentz Center (Virtual)
July 6 - 10, 2020 I attended the Applied Category Theory Conference. MIT (Virtual)
August 5 – 9, 2019 Summer school on Persistent homology and Barcodes Schloss Rauischholzhausen
June 12 - 14, 2019 Workshop on Geometry, Topology, and Computation Heidelberg University
January - April, 2019 Guest at UC Berkeley UC Berkeley
August - Oktober, 2018 Research Internship in the group of Bernd Sturmfels at MPI MiS, Leipzig. MPI MiS, Leipzig.
August 13 - 17, 2018 Workshop: Numerical Computing in Algebraic Geometry MPI MiS, Leipzig.
June 12 - 15, 2018 Workshop: The Roots of Topology University of Chicago



When What Where
October 2023 - April 2024 Organizer of Homotopical Category Theory with Christian Dahlhausen Heidelberg University
October 2023 - April 2024 Teaching Assistant for Algebraic Topology I Heidelberg University


When What Where
October 2022 - April 2023 Teaching Assistant for Algebraic Geometry I Heidelberg University
April 2022 - Oktober 2022 Teaching Assistant for Algebraic Topology II Heidelberg University
October 2021 - April 2022 Teaching Assistant for Algebraic Topology I Heidelberg University
October 2020 - April 2021 Teaching Assistant for Set Theoretic Topology Heidelberg University
February - June 2020 Teaching Assistant for the ACT Adjoint School Online and at MIT
Oktober 2019 - April 2020 Teaching Assistant for Differential Topology I Heidelberg University
April - Oktober 2018 Question Designer for the KeKs system. Heidelberg University
Oktober 2016 - April 2017 Teaching Asisstant for Algebra I Heidelberg University


Ruprecht-Karls-Universität Heidelberg
Institut für Mathematik
Raum 03.306