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Niklas Hellmer

I read the news today - oh, boy/ Four thousand holes in Blackburn, Lancashire/ And though the holes were rather small/ They had to count them all/ Now they know how many holes it takes to fill the Albert Hall
-The Beatles, A Day In The Life
In Breselenz, Riemann's birthplace. I completed my PhD in February 2025. Here you can find my thesis "Probability meets Topological Data Analysis", which is concerned with metrics for persistence diagrams and modules, Dowker complexes and interactions of TDA with statistics. Watch my AATRN seminar talk: While I have left acadmia for a position as IT consultant focused on data engineering, I'm still happy to chat about research.

Personal Information

(deprecated, only kept for nostalgical reasons) Dioscuri Centre in Topological Data Analysis
Instytut Matematyczny PAN
Room 16
Sniadeckich 8, 00-656 Warszawa
@
ORCID

Here is a recent CV.

News

25/04/2025:
- Our article "Density Sensitive Bifiltered Dowker Complexes via Total Weight" (joint with Jan Spaliński) is accepted for publication in Hopotopy, Homology and Applications.
27/02/2025:
- The scientific council officially confirmed the doctoral degree.
07/02/2025:
- I successfully defended my PhD.
27/05/2024:
- Preprint "Density Sensitive Bifiltered Dowker Complexes via Total Weight" (joint with Jan Spaliński) on the ArXiv.
10/01/2024:
- Preprint "When Do Two Distributions Yield the Same Expected Euler Characteristic Curve in the Thermodynamic Limit?" (joint with Tobias Fleckenstein) on the ArXiv.
13/12/2023:
- Giving a talk at the AATRN semnar.
09/11/2023:
- "Topology-driven goodness of fit tests in arbitrary dimensions" published online at Stat Comput.
07/11/2023:
- Giving a talk at the TU Munich applied topology seminar.
23/10/2023:
- Giving a talk at the University of Michigan Dearborn Math and Statistics colloquium.
24/09/2023:
- Starting my visit to Bastian Rieck's AIDOS lab at Helmholtz Munich (stay until christmas)
08/05/2023:
- "Bottleneck Profiles and Discrete Prokhorov Metric for Persistence Diagrams" released online at DCG.
28/10/2022:
- Preprint "Topology-Driven Goodness-of-Fit Tests in Arbitrary Dimensions" on the ArXiv.
10.-14.10.2022
- Attending the workshop on geometry, topology and statistics at Institut Henri Poincare, Paris.
winter term 2022/23
- teaching recitation classes for Analysis I for WNE.
28.-30.09.2022
- Attending the TDA Workshop in Heidelberg, giving a "lightning talk" an Goodness-of-fit testing using Topology.
23/04/2022:
- Giing a talk at the 4th (Virtual) International Conference on Trauma Surgery Technology 2022, dedicated to Mathematics in Medical Diagnostics .
04/03/2022:
- Teaching labs for Pawel's course "Invitation to TDA".
10/11/2021:
- Giving a talk at the Dioscuri Seminar.
22/10/2021:
- Giving a talk in Piotr Hajac's Noncommutative Geometry Seminar about Persistent Homology: Algebra, Metrics, Stability.
04/10/2021:
- Back in office!
21/07/2021:
- Talk at the Lorentz Centre Workshop on Metrics in Multiparameter Persistence.
7/06/2021:
- Preprint "Bottleneck Profiles and Discrete Prokhorov Metric for Persistence Diagrams" on the ArXiv.
30/04/2021:
- Poster presentation "Discrete Prokhorov Metric for Persistence Diagrams" at TDA workshop at IMSI.
21/02/2021:
- Talk about "Discrete Prokhorov Metric for Persistence Diagrams" at APATG.
15/10/2020:
- Official inauguration of the Dioscuri Centre.
1/10/2020:
- I move to Dioscuri TDA at IMPAN.
29/09/2020:
- Talk about "New Metrics for Persistence Diagrams" at the Second Symposium on Machine Learning and Dynamical Systems. Video.
21/08/2020:
- OxCOVID19DB preprint on medRxiv.

Publications

(BibTeX)
[5]
N. Hellmer and J. Spaliński, ‘Density Sensitive Bifiltered Dowker Complexes via Total Weight’. arXiv, May 24, 2024. Available: http://arxiv.org/abs/2405.15592. Accepted at Homotopy, Homology and Applications.
[4]
T. Fleckenstein and N. Hellmer, ‘When Do Two Distributions Yield the Same Expected Euler Characteristic Curve in the Thermodynamic Limit?’ arXiv, Jan. 09, 2024. Available: http://arxiv.org/abs/2401.04580
[3]
P. Dłotko, N. Hellmer, Ł. Stettner, and R. Topolnicki, ‘Topology-driven goodness-of-fit tests in arbitrary dimensions’, Stat Comput, vol. 34, no. 1, p. 34, Nov. 2023, doi: 10.1007/s11222-023-10333-0.
[2]
P. Dłotko and N. Hellmer, ‘Bottleneck Profiles and Discrete Prokhorov Metrics for Persistence Diagrams’, Discrete Comput Geom, May 2023, doi: 10.1007/s00454-023-00498-w.
[1]
A. Mahdi et al., ‘OxCOVID19 Database, a multimodal data repository for better understanding the global impact of COVID-19’, Scientific Reports, vol. 11, no. 1, Art. no. 1, Apr. 2021, doi: 10.1038/s41598-021-88481-4.