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!
Currently I am working on my PhD thesis on stratified homotopy theory at Heidelberg University under the supervision of Markus Banagl. I am also the (upcoming) principal investigator for the exploratory project "Invariants of Persistent Stratified Homotopy Types" at the excellence cluster "Structures" at Uni Heidelberg. When I don't do mathematics, I'm an avid cook, traveller and boardgame geek.
Very broadly speaking, I am interested in anything that happens at the interaction of homotopy theory, geometry, algebra and (higher) category theory. Specifically, I am currently focussing my research on investigating the homotopy theory of stratified spaces. Besides the obvious theoretical disciplines a mathematician interested in such topics might focus on (most prominently, algebraic topology in my case), my focus lies also lies on how to use theoretical insights in applied topology.
Below is a list some past and current projects.
| Topic | Coauthors | |
|---|---|---|
| I am currently the principal investigator for the exploratory project "Invariants of Persistent Stratified Homotopy Types". Work will begin some time early next year. | Bernadette Stolz, Markus Banagl | Excellence Cluster Structures - Uni Heidelberg |
| 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 |
|---|---|---|
| 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 |
| When | What | Where |
|---|---|---|
| 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 |
|---|---|---|
| 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 |
| 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 |
