Welcome

Hey, my name is Lukas. I am a postdoc at the Mathematical Institute of Oxford University.
Welcome to my website!

About Me

Currently, I am a postdoc at Oxford University. When I don't do mathematics, I'm an avid cook, traveller and boardgame geek.

Academic Interests

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.

Teaching

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

Research

Below is a list some past and current projects.

Topic Coauthors PDF
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 To appear in Journal of Algebraic and Geometric Topology;
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 (Formerly '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

Travelling

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

Upcoming:

When What Where
March 16-20, 2026 Research visit at MPI Dresden Heather Harrington's group at MPI Dresden
April 23, 2026 Invited speaker at the higher invariants seminar in Regensburg University of Regensburg
May 18-21, 2026 Foundations of Computational Geometry and Topology ICERM, Brown University
June 2-6, 2026 Speaker at SoCG 2026 Rutgers University

Past:

When What Where
January 26-30, 2026 Speaker at Algebraic Topology: Methods, Computation, and Science (ATMCS 12) MPI Leipzig
December 11, 2025 Speaker at the SALTO Kick-Off Workshop "Higher-order interactions at the crossroads of geometry and topology Laboratoire de Mathématiques d’Orsay, Université Paris-Saclay (Paris)
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

Teaching

Current:

When What Where
Ongoing Organizer for a reading course on the theory of constructible sheaves University of Oxford and MPI Dresden

Reading course on constructible sheaves – details

Start: 18 February 2026
Time: 12:00–13:30 GMT / 13:00–14:30 CET
Place: Room L5, Andrew Wiles Building
Zoom: See here
Material: will be made available here
Mailing list: Email me to be added

Schedule

Date Plan
18.02.2026 Grand Conspiracy: Informal intro to constructible sheaves in persistence — Lukas Waas
25.02.2026 Ten things sheaves don't want you to know: Basics of sheaf theory — Vukasin Stojisavljevic
04.03.2026 TBD
11.03.2026 TBD
18.03.2026 – 28.04.2026 Term break in Oxford (we may continue during the break)
29.04.2026 First session in Trinity Term

Past:

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

Contact

Oxford University
Department of Mathematics
Room S3.12 Andrew Wiles Building
Woodstock Road