Vrije Universiteit
(VU University Amsterdam)
Department of Mathematics
Faculteit der Exacte Wetenschappen
De Boelelaan 1111
1081 HV Amsterdam
Short bio
I am an assistant professor (Universitair Docent) at the department of mathematics at the Vrije Universiteit (VU) in Amsterdam. I held a 'tenure track' position from 2018 to 2022. Prior to this, I was a postdoc at TU Munich working with Ulrich Bauer (2016-2018). I defended my PhD at NTNU in December 2015 under the supervision of Nils A. Baas.
Research
I work within the field of topological data analysis: a relatively recent branch of mathematics in which topological signatures are assigned to data. Enjoying being at both the pure and applied side of mathematics, my research includes pure elements such as representation theory of quivers, as well as more computational aspects, and applications towards the sciences.
Pepijn Roos Hoefgeest (PhD, VU) [2018-2023]: thesis available here.
Media/Documents
I recently (2025) gave a talk at the GEOTOP-A seminar. The talk was recorded.
The lecture notes from the Mastermath course Topological Data Analaysis (2024) can be found here. The text is gradually getting in better shape. Thanks to the students for correcting numerous errors!
A tutorial on multiparameter persistence given at GETCO 2022 has been recorded and uploaded to Youtube.
(With R. Dong) Cheeger Inequalities for the Persistent Laplacian. arXiv.
Surveys
(With Abiad et al.) Hypergraphs and simplicial complexes in focus: A roadmap for future research in higher-order interactions. Journal of Physics: Complexity (2026) (doi).
(With M. Lesnick) An Introduction to Multiparameter Persistence. EMS Series of Congress Reports (2023, ICRA 2020, by invitation) (doi, arXiv).
In Press
(With U. Bauer, S. Oppermann, J. Steen) On the additive image of the zeroth persistent homology. Trans. London Math. Soc., 13: e70027, (doi, arXiv).
(With R. Dong) The persistent Laplacian of non-branching complexes. Foundations of Data Science 10 (2026) 53--89, (doi, arXiv).
(With S. Oppermann and S. Oudot) Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions and Rank-Exact Resolutions. Found Comput Math (2024) (doi, arXiv).
(With C. Hirsch) On the consistency and asymptotic normality of multiparameter persistent Betti numbers. J Appl. and Comput. Topology 8, 1465--1502 (2024) (doi, arXiv)
(With U. Bauer and B. Fluhr) Universality of the Bottleneck Distance for Extended Persistence Diagrams. J Appl. and Comput. Topology 8, (2024) (doi, arXiv)
(With S. Oppermann, S. Oudot, and L. Scoccola) On the bottleneck stability of rank decompositions of multi-parameter persistence modules. Advances in Mathematics 451 (2024) (doi, arXiv).
(With V. Lebovici and S. Oudot) Local characterizations for decomposability of 2-parameter persistence modules.
Algebr Represent Theor 26, 3003–3046 (2023) (doi, arXiv).
(With V. Lebovici and S. Oudot) On rectangle-decomposable 2-parameter persistence modules. Discrete Comput Geom 68, 1078--1101 (2022) [by invitation], (doi).
(With H. B. Bjerkevik and M. Kerber) Computing the interleaving distance is NP-hard. Found Comput Math 20, 1237--1271 (2020), (doi).
(With W. Crawley-Boevey) Decomposition of persistence modules. Proc. Amer. Math. Soc. 148 (2020). 581-4596, (doi).
(With U. Bauer, S. Oppermann and J. Steen) Cotorsion torsion triples and the representation theory of filtered hierarchical clustering. Advances in Mathematics 369 (2020), (doi).
(With M. Lesnick) Algebraic stability of zigzag persistence modules. Algebraic & Geometric Topology 18 (2018) 3133-3204, (doi).
(With G. Spreemann, B. Dunn and N. A. Baas) Using persistent homology to reveal hidden covariates in systems governed by the kinetic Ising model. Physical Review E, 2018, 97.3: 032313, (doi).
Interval decomposition of infinite zigzag persistence modules. Proc. Amer. Math. Soc. 145 (2017), 3571-3577, (doi).
(With G. Spreemann) Approximating persistent homology in Euclidean space through collapses. G. AAECC (2015) 26:73, (doi).
(With R. Zhang, V. Sachnev, H. J. Kim and J. Heo) An Efficient Embedder for BCH Coding for Steganography. IEEE Transactions on Information Theory ( Volume: 58 , Issue: 12 , Dec. 2012 ), (doi).
Older Preprints
(With U. Bauer and B. Fluhr) Structure and Interleavings of Relative Interlevel Set Cohomology. arXiv.
(With J. Curry and E. Munch) A Relative Theory of Interleavings. arXiv.
Conference proceedings
(With L. Beers) Extremal Betti Numbers and Persistence in Flag Complexes. The 41st International Symposium on Computational Geometry (SoCG 25), (doi, arXiv).
(With D. Loiseaux, L. Scoccola, M. Carriere, and S. Oudot) Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures. Advances in Neural Information Processing Systems 36 (NeurIPS 2023) (nips.cc, arXiv).
(With S. Oppermann and S. Oudot) Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions and Rank-Exact Resolutions. 38th International Symposium on Computational Geometry (SoCG 2022), (doi).
(With V. Lebovici and S. Oudot) On rectangle-decomposable 2-parameter persistence modules. 36th International Symposium on Computational Geometry (SoCG 2020), (doi).
(With H. B. Bjerkevik) Computational Complexity of the Interleaving Distance. 34th International Symposium on Computational Geometry (SoCG 2018), (doi).
