Hey, my name is Lukas. I am a postdoc at the Mathematical Institute of Oxford University.
Welcome to my website!
Currently, I am a postdoc at Oxford University and the PI for the exploratory project "Invariants of Persistent Stratified Homotopy Types" at the Excellence Cluster Structures - Uni Heidelberg. When I don't do mathematics, I'm an avid cook, traveller and boardgame geek.
My research interests lie within the interior and at the boundary of the 2-simplex spanned by homotopy theory, stratified spaces and topological data analysis.
Below is a list some past and current projects.
| Topic | Coauthors | |
|---|---|---|
| My PhD-Thesis. There is a lot of overlap with the work below, but the part on generalized simple homotopy theory is new, and the first introductory chapter features an introduction to stratified homotopy theory. | - | Thesis |
| Presenting the topological stratified homotopy hypothesis | - | arXiv |
| Combinatorial models for stratified homotopy theory | - | arXiv |
| On the homotopy links of stratified cell complexes | - | arXiv |
| On stratifications and poset-stratified spaces | Shoji Yokura and Jonathan Woolf | arXiv |
| From Samples to Persistent Stratified Homotopy Types | Tim Mäder | Journal of Applied and Computational Topology |
| From homotopy links to stratified homotopy theories | Sylvain Douteau | arXiv (to appear in Mémoires de la SFM) |
| Abelian categories of finitely encodable multiparameter persistence modules (Formely 'Notes on Multiparameter Persistence Modules and Amplitudes') | - |
arXiv; |
| A property of the interleaving distance for sheaves | Francois Petit, Pierre Schapira | Bulletin of the London Mathematical Society |
| Amplitudes on abelian categories | Barbara Giunti, John S. Nolan, Nina Otter | Journal of Pure and Applied Algebra |
| Master Thesis: Stratified Homotopy Theory and a Whitehead Group for Stratified Spaces | - | arXiv |
Below is a list of past and upcoming (academic) travel and talks.
| When | What | Where |
|---|
| When | What | Where |
|---|---|---|
| October 6, 2025 | Speaker at the Young homotopy-theorist meeting | CMS, Bayes Centre, Edinburgh |
| July 22, 2025 | Speaker at the TP25TD | OIST Okinawa |
| July 10, 2025 | Invited speaker at the Mathematisches Seminar | Universität Kiel |
| June 16, 2025 | Invited speaker at the TDA Week in Kyoto | Kyoto University |
| March 5, 2025 | Invited speaker at the Algebra and Topology Seminar | University of Copenhagen |
| February, 2025 | Invited speaker at Department of Machine Learning and Systems Biology | MPI für Biochemie, München |
| November 25, 2025 | Invited speaker at Séminaire GT3 of the Strasbourg geometry group | Strasbourg |
| September 16 - 20, 2024 | Invited speaker at the conference Structures on Singular Spaces through the Lens of Characteristic Classes | Heidelberg University |
| June 24-28, 2024 | I attended the Masterclass "Exit paths and stratified homotopy types" | University of Copenhagen |
| May 24 , 2024 | Invited speaker at the Applied Topology Seminar | Oxford University |
| May 6 – 10, 2024 | I attended the conference Higher Algebra, Geometry, and Topology | CIRM |
| 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 |
| Dec 08, 2023 | Speaker at the STRUCTURES JOUR FIXE on my work on stratified TDA | Structures Uni Heidelberg |
| 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, 2023 | 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 |
| 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 |
|---|
| When | What | Where |
|---|---|---|
| October 2023 - April 2024 | Teaching Assistant for Algebraic Topology I | Heidelberg University |
| 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 |
| 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 |
