I am an assistant professor at the department of mathematics at the Vrije Universiteit (VU) in Amsterdam. Before coming here I was a postdoc at TU Munich working with Ulrich Bauer. I defended my PhD at the Norwegian University of Science and Technology in December 2015 under the supervision of Nils A. Baas.
ResearchI 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.
Recent and Upcoming Events
- Together with Ulrich Bauer and Michael Lesnick I am organizing a workshop at the Lorentz Center in Leiden: Metrics in Multiparameter Persistence.
- I will give a lecture series at ICRA 2020 (which unfortunately has been postponed).
- Linear Algebra.
- Master Seminar in Analysis and Dynamical Systems.
- Pepijn Roos Hoefgeest
Media/Documents
- The lecture notes from the Mastermath course Topological Data Analaysis can be found here. The text will be polished at some point. Thanks to the students for correcting numerous errors!
- Two lectures from the IMA Workshop on Multiparameter Persistence have been published online. The first one, Quiver Representation Theory + Multiparameter Persistence, gives a self-contained introduction to the role of representation theory in topological data analysis. In my second lecture, Multiparameter Interleavings, I give an introduction to interleavings in the context of one- and multiparameter persistent homology.
- 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
Preprints
- (With U. Bauer and B. Fluhr) Universality of the Bottleneck Distance for Extended Persistence Diagrams. arXiv.
- (With J. Curry and E. Munch) A Relative Theory of Interleavings. arXiv.
- (With V. Lebovici and S. Oudot) On rectangle-decomposable 2-parameter persistence modules, arXiv, accepted to The 36th International Symposium on Computational Geometry.
- (With H. B. Bjerkevik and M. Kerber) Computing the interleaving distance is NP-hard, arXiv, accepted for publication in Foundations of Computational Mathematics.
- (With W. Crawley-Boevey) Decomposition of persistence modules, arXiv, accepted for publication in Proceedings of the American Mathematical Society.
In Press
- (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 H. B. Bjerkevik) Computational Complexity of the Interleaving Distance.
34th International Symposium on Computational Geometry (SoCG 2018), Vol. 99. (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)
- (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)
Past Events
- 33rd Summer Cenference on Topology and its Applications, Johannesburg, July 1-4 2019
Past Teaching:
- Summer 2020: Modelling of Dynamical Systems
- Spring 2020: Topological Data Analysis (Mastermath)
- Spring 2029: Master Seminar in Analysis and Dynamical Systems.
- Fall 2019: Numerical Methods.
- Summer 2019: Modelling of Dynamical Systems
- Spring 2019: Numerical Methods.
- Spring 2019: Master Seminar in Analysis and Dynamical Systems.
- Fall 2018: Calculus 1 at the Amsterdam University College (AUC).
Publications
Preprints- (With U. Bauer and B. Fluhr) Universality of the Bottleneck Distance for Extended Persistence Diagrams. arXiv.
- (With J. Curry and E. Munch) A Relative Theory of Interleavings. arXiv.
- (With V. Lebovici and S. Oudot) On rectangle-decomposable 2-parameter persistence modules, arXiv, accepted to The 36th International Symposium on Computational Geometry.
- (With H. B. Bjerkevik and M. Kerber) Computing the interleaving distance is NP-hard, arXiv, accepted for publication in Foundations of Computational Mathematics.
- (With W. Crawley-Boevey) Decomposition of persistence modules, arXiv, accepted for publication in Proceedings of the American Mathematical Society.
- (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 H. B. Bjerkevik) Computational Complexity of the Interleaving Distance.
34th International Symposium on Computational Geometry (SoCG 2018), Vol. 99. (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) - (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)
- 33rd Summer Cenference on Topology and its Applications, Johannesburg, July 1-4 2019
- Summer 2020: Modelling of Dynamical Systems
- Spring 2020: Topological Data Analysis (Mastermath)
- Spring 2029: Master Seminar in Analysis and Dynamical Systems.
- Fall 2019: Numerical Methods.
- Summer 2019: Modelling of Dynamical Systems
- Spring 2019: Numerical Methods.
- Spring 2019: Master Seminar in Analysis and Dynamical Systems.
- Fall 2018: Calculus 1 at the Amsterdam University College (AUC).