Magnus Bakke Botnan

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.

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.

My research is supported by a VIDI career grant (€850.000) (news item, official announcement).

Recent and Upcoming Events

• Rui Dong is hired for a one year postdoctoral commitment to my VIDI project.
• We are organizing another round of the applied topology day.
• The lecture notes have been updated again (see below).
• Recently I co-authored An Introduction to Multiparameter Persistence with Mike Lesnick.

• Complex Analysis.

Research group

• Hannah Rocio Santa Cruz Baur (Postdoc, VU) [2025-] (joint CTA^2 postdoc).
• Rui Dong (Postdoc, VU) [2025-].
• Enes Devecio (PhD, VU) [2025-].

• 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.
• My keynote lecture at the BIRS Workshop on Multiparameter Persistent Homology has been published online: From One to Two Parameters. This talk offers an accessible introduction to my research in multiparameter persistence.

Publications

1. (With R. Dong) The persistent Laplacian of non-branching complexes. arXiv.
2. (With L. Beers) Extremal Betti Numbers and Persistence in Flag Complexes. arXiv.
   Accepted to the 41st International Symposium on Computational Geometry (SoCG 2025).
3. (With U. Bauer, S. Oppermann and J. Steen) On the additive image of 0th persistent homology. arXiv.
4. (With H.B. Bjerkevik) Computing p-presentation distances is hard. arXiv.
   To appear in Discrete and Computational Geometry.
5. (With U. Bauer and B. Fluhr) Structure and Interleavings of Relative Interlevel Set Cohomology. arXiv.
6. (With J. Curry and E. Munch) A Relative Theory of Interleavings. arXiv.

1. (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).
2. (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)
3. (With U. Bauer and B. Fluhr) Universality of the Bottleneck Distance for Extended Persistence Diagrams.
   J Appl. and Comput. Topology 8, (2024) (doi, arXiv)
4. (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).
5. (With V. Lebovici and S. Oudot) Local characterizations for decomposability of 2-parameter persistence modules.
   Algebr Represent Theor 26, 3003–3046 (2023) (doi, arXiv).
6. (With M. Lesnick) An Introduction to Multiparameter Persistence.
   EMS Series of Congress Reports (2023, ICRA 2020, by invitation), (doi, arXiv).
7. (With V. Lebovici and S. Oudot) On rectangle-decomposable 2-parameter persistence modules.
   Discrete Comput Geom 68, 1078--1101 (2022) [by invitation], (doi).
8. (With H. B. Bjerkevik and M. Kerber) Computing the interleaving distance is NP-hard.
   Found Comput Math 20, 1237--1271 (2020), (doi).
9. (With W. Crawley-Boevey) Decomposition of persistence modules.
   Proc. Amer. Math. Soc. 148 (2020). 581-4596, (doi).
10. (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).
11. (With M. Lesnick) Algebraic stability of zigzag persistence modules.
    Algebraic & Geometric Topology 18 (2018) 3133-3204, (doi).
12. (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).
13. Interval decomposition of infinite zigzag persistence modules.
    Proc. Amer. Math. Soc. 145 (2017), 3571-3577, (doi).
14. (With G. Spreemann) Approximating persistent homology in Euclidean space through collapses.
    G. AAECC (2015) 26:73, (doi).
15. (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).

1. (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).
2. (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).
3. (With V. Lebovici and S. Oudot) On rectangle-decomposable 2-parameter persistence modules.
   36th International Symposium on Computational Geometry (SoCG 2020), (doi).
4. (With H. B. Bjerkevik) Computational Complexity of the Interleaving Distance.
   34th International Symposium on Computational Geometry (SoCG 2018), (doi).

Supervised bachelor and masters theses

1. Donny Peeters (Master, UvA, 2021) Metrics in Multiparameter Persistent Homology.
2. Francesco Cenzato (Master, Leiden, 2021) Homological clustering of simplicial complexes.
3. Yoav Eshel (Bachelor, VU, 2022) On the Decomposition of Pointwise Finite Dimensional Persistence Modules.
4. Nikolaos Chatzis (Master, UvA, 2023) A topological approach to polynomial regression.
5. Sliem el Ela (Master, UvA, 2023) From Primordials to Persistence: A Dual Exploration of Multiparameter Topology and Cosmic Origins.
6. Brandon Leahy (Master, UvA, 2024) Rank Exact Resolutions of Representations in Topological Data Analysis.
7. Mark Lapidus (Bachelor, VU, 2024), Topological data analysis in crystallography.

1. 33rd Summer Cenference on Topology and its Applications. Johannesburg, July 2019.
2. Metrics in Multiparameter Persistence. Leiden, July 2021.
3. Randomness Unleashed Geometry, Topology and Data. Groningen, September 2021.
4. Applied Topology Day. Amsterdam, September 2022.
5. Workshop: Interactions between representation theory and topological data analysis. Oslo, December 2022.
6. Recent developments in multiparameter persistence. Eindhoven, July 2023.
7. Applied Topology Day. Amsterdam, September 2023.

1. Fall 24: Calculus 2
2. Fall 2023/24: Differential equations
3. Spring 2021/22: Complex Analysis
4. Fall 2020/21/22: Master Seminar in Analysis and Dynamical Systems
5. Fall 2020/21/22/23: Linear Algebra
6. Spring 2020/22/24: Topological Data Analysis (Mastermath)
7. Fall 2019: Numerical Methods.
8. Summer 2019/20/21: Modelling of Dynamical Systems
9. Spring 2019: Numerical Methods.
10. Spring 2019/20: Master Seminar in Analysis and Dynamical Systems.
11. Fall 2018: Calculus 1 at the Amsterdam University College (AUC).