Welcome

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

About Me

Since November 2025, I have been a postdoctoral research associate in the Topology Group at the Mathematical Institute, University of Oxford.

I completed my PhD in mathematics at Heidelberg University in April 2025. From May to October 2025, I was principal investigator of the STRUCTURES exploratory project Invariants of Persistent Stratified Homotopy Types at Heidelberg.

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

My teaching includes courses and seminars at Heidelberg, a reading course on constructible sheaves, and examining at Oxford.

Research

Below is a list of some past and current projects.

TopicCoauthorsLinks
PhD thesis (2025): Stratified Homotopy Theory and Generalized Simple Homotopy Theory: Foundations, Applications and Intersections
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.		—PDF · University repository
Function-Rips complexes in persistent homotopy theory: Stability and persistent Latschev theoremsSteve OudotarXiv:2603.23460 (2026)
Expanded version of the following paper.
A Persistent Version of Latschev’s TheoremSteve OudotSoCG 2026, LIPIcs 367, 82:1–82:17
Presenting the topological stratified homotopy hypothesis—arXiv:2403.07686 (2024)
Combinatorial models for stratified homotopy theory—arXiv:2403.06280 (2024)
On the homotopy links of stratified cell complexes—arXiv:2403.06272 (2024)
On stratifications and poset-stratified spacesJon Woolf, Shoji YokuraAlgebraic & Geometric Topology 26 (2026), 2519–2538; arXiv
From samples to persistent stratified homotopy typesTim MäderJournal of Applied and Computational Topology 8 (2024), 761–838
From homotopy links to stratified homotopy theoriesSylvain DouteauForthcoming in Mémoires de la Société Mathématique de France (SMF). arXiv
Notes on abelianity of categories of finitely encoded persistence modules—arXiv:2407.08666 (2024)
A property of the interleaving distance for sheavesFrançois Petit, Pierre SchapiraBulletin of the London Mathematical Society 57 (2025), 137–149
Amplitudes in persistence theoryBarbara Giunti, John S. Nolan, Nina OtterJournal of Pure and Applied Algebra 228 (2024), 107770
Master thesis (2020): Stratified Homotopy Theory and a Whitehead Group for Stratified Spaces—arXiv

Travelling

Past and upcoming academic travel and talks.

Upcoming

WhenWhatWhere
October 20, 2026Invited speaker at the Algebraic Topology SeminarUniversity of Warwick
December 2026 (planned)Research visit with Guglielmo NoceraInstitut des Hautes Études Scientifiques (IHÉS), Bures-sur-Yvette

Past

WhenWhatWhere
October 1–2, 2026Speaker at the 39th British Topology MeetingUniversity of Oxford
July 2026Invited speaker at the Transalpine Topology Tetrahedron (TTT124)University of Liverpool
June 2-6, 2026Speaker at SoCG 2026 Rutgers University
May 18-21, 2026Foundations of Computational Geometry and Topology ICERM, Brown University
May 2026Research visit with Bei WangScientific Computing and Imaging Institute, University of Utah
April 23, 2026Invited speaker at the higher invariants seminar in Regensburg University of Regensburg
March 16-20, 2026Research visit at MPI DresdenHeather Harrington's group at MPI Dresden
January 26-30, 2026Speaker at Algebraic Topology: Methods, Computation, and Science (ATMCS 12) MPI Leipzig
January 2026Speaker at the Applied Topology SeminarUniversity of Oxford
December 11, 2025Speaker 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)
November 25, 2025Invited speaker at Séminaire GT3 of the Strasbourg geometry group Strasbourg
October 6, 2025Speaker at the Young homotopy-theorist meeting CMS, Bayes Centre, Edinburgh
July 22, 2025Speaker at the TP25TD OIST Okinawa
July 10, 2025Invited speaker at the Mathematisches Seminar Universität Kiel
June 16, 2025Invited speaker at the TDA Week in KyotoKyoto University
March 5, 2025Invited speaker at the Algebra and Topology Seminar University of Copenhagen
February, 2025Invited speaker at Department of Machine Learning and Systems Biology MPI für Biochemie, München
September 16 - 20, 2024Invited speaker at the conference Structures on Singular Spaces through the Lens of Characteristic Classes Heidelberg University
June 24-28, 2024I attended the Masterclass "Exit paths and stratified homotopy types" University of Copenhagen
May 24, 2024Invited speaker at the Applied Topology Seminar Oxford University
May 6 – 10, 2024I attended the conference Higher Algebra, Geometry, and Topology CIRM
March 21, 2024Invited speaker for Journées de topologie algébrique, géométrique et quantique en Picardie Université de Picardie Jules Verne
March 7, 2024Invited speaker at the Après-midi de Topologie Université Sorbonne Paris Nord
December 8, 2023Speaker at the STRUCTURES JOUR FIXE on my work on stratified TDA Structures Uni Heidelberg
October 17, 2023Speaker at the EPFL Topology Seminar on my work on pure and applied stratified homotopy theory EPFL Lausanne
September 18 - 22, 2023Speaker at the Conference on Characteristic Classes and Singular Spaces on my work on a tractable version of the stratified homotopy hypothesisKiel University
September 7 - 16, 2023Research visit at the Institut de Recherche en Informatique FondamentaleInstitut de Recherche en Informatique Fondamentale, Paris
August 20 - 25, 2023Poster presentations on "From Samples to Persistent Stratified Homotopy Types" at the ICIAM 2023 Waseda University, Tokyo
July 24 - 28, 2023Poster presentation on my work on a tractable version of the stratified homotopy hypothesis at the "Young Topologists Meeting 2023" EPFL Lausanne
June 5 - 9, 2023I attended the conference "A Panorama of Homotopy Theory" University of Oxford
October 2022Invited speaker at the Persistence Sheaves and Homotopy SeminarOnline, hosted by EPFL
June 19 - 24, 2022Poster presentations on "Amplitudes on abelian categories" and "From Samples to Persistent Stratified Homotopy Types" at the ATMCS 10 University of Oxford
June 13 - 17, 2022Research Visit and Speaker at the Topology Seminar of Matematiska institutionen, Stockholm University: (Matematiska institutionen, Stockholm University)
August 16 - 20, 2021I was a (spontaneous substitute) speaker at the SIAM: Conference on Applied Algebraic Geometry. (Virtual)
July 19–22, 2021I attended the Workshop Metrics in Multiparameter Persistence.Lorentz Center (Virtual)
July 6 - 10, 2020I attended the Applied Category Theory Conference.MIT (Virtual)
August 5–9, 2019Summer school on Persistent homology and Barcodes Schloss Rauischholzhausen
June 12 - 14, 2019Workshop on Geometry, Topology, and Computation Heidelberg University
January - April, 2019Guest at UC BerkeleyUC Berkeley
August - October, 2018Research Internship in the group of Bernd Sturmfels at MPI MiS, Leipzig. MPI MiS, Leipzig.
August 13 - 17, 2018Workshop: Numerical Computing in Algebraic Geometry MPI MiS, Leipzig.
June 12 - 15, 2018Workshop: The Roots of TopologyUniversity of Chicago

Teaching

Current and recent

WhenWhatWhere
September–October 2026Part C thesis examinerUniversity of Oxford
June 2026–presentExaminer for Computational Algebraic TopologyUniversity of Oxford
February 2026–presentOrganiser and teacher of an ongoing reading course on constructible sheavesUniversity of Oxford and MPI Dresden

Past

WhenWhatWhere
October 2023 - April 2024Teaching Assistant for Algebraic Topology IHeidelberg University
October 2023 - April 2024Teacher and organiser of Homotopical Category Theory with Christian DahlhausenHeidelberg University
October 2022 - April 2023Teaching Assistant for Algebraic Geometry IHeidelberg University
April 2022 - October 2022Teaching Assistant for Algebraic Topology IIHeidelberg University
October 2021 - April 2022Teaching Assistant for Algebraic Topology IHeidelberg University
October 2020 - April 2021Teaching Assistant for Set-Theoretic TopologyHeidelberg University
February - June 2020Teaching Assistant for the ACT Adjoint SchoolOnline and at MIT
October 2019 - April 2020Teaching Assistant for Differential Topology IHeidelberg University
April - October 2018Question Designer for the KeKs system.Heidelberg University
October 2016 - April 2017Teaching Assistant for Algebra IHeidelberg University

Service and Funding

Academic service

WhenRole
2026–2027Programme committee member, International Symposium on Computational Geometry (SoCG 2027)
2026Workshop organiser, STRATIFYING KIEL: Stratified Spaces from Higher Category Theory to Applied Topology, Kiel University
July 2026Working group organiser, Computable Invariants of Quiver Representations, Lorentz Center, Leiden

Selected funding

WhenAward / project
2026Visiting Research Fellowship (SSHN), French Embassy in the United Kingdom, for Functorial resolution of singularities for stratified spaces, supporting a research stay at IHÉS with Guglielmo Nocera.
2024–2025Exploratory Project funding, STRUCTURES Cluster of Excellence, Heidelberg University, for Invariants of Persistent Stratified Homotopy Types. Principal investigator, May–October 2025.
2021–2024Doctoral scholarship, Landesgraduiertenförderung Baden-Württemberg.
2015–2020Fellowship, Studienstiftung des deutschen Volkes.

Contact

Mathematical Institute
University of Oxford
Room S3.12, Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford OX2 6GG
United Kingdom

lukas.waas@maths.ox.ac.uk