Alexander Rolle

Short biography

I am a postdoctoral researcher in the Mathematics department at The Technical University of Munich, working with Ulrich Bauer. From September 2019 to September 2021 I was a postdoc with Michael Kerber at TU Graz, Austria. In August 2019 I finished a PhD in Mathematics at The University of Western Ontario, Canada, supervised by Rick Jardine.

Research interests

My research interests are in applied topology, especially applications to statistics, data analysis, and machine learning.

Publications and preprints

Diverse 3D cellular patterns underlie the development of Cardamine hirsuta and Arabidopsis thaliana ovules, with Tejasvinee Atul Mody, Nico Stucki, Fabian Roll, Ulrich Bauer, and Kay Schneitz (2023). Preprint. Available at bioRxiv.
Persistable: persistent and stable clustering, with Luis Scoccola (2023). Journal of Open Source Software. Available at JOSS.
Compression for 2-parameter persistent homology, with Michael Kerber and Ulderico Fugacci (2023). Computational Geometry. Available at ScienceDirect (open access) and arXiv.
A unified view on the functorial nerve theorem and its variations, with Ulrich Bauer, Michael Kerber, and Fabian Roll (2023). Expositiones Mathematicae. Available at ScienceDirect and arXiv.
The degree-Rips complexes of an annulus with outliers (2022). SoCG 2022. Available at DROPS and arXiv.
Fast minimal presentations of bi-graded persistence modules, with Michael Kerber (2021). ALENEX 2021. Available at siam and arXiv.
Multi-parameter hierarchical clustering and beyond (extended abstract) (2020). Topological Data Analysis and Beyond Workshop at NeurIPS 2020. Available at OpenReview.
Stable and consistent density-based clustering, with Luis Scoccola (2020). Preprint. Available at arXiv.
Torsors over simplicial schemes (2019). PhD thesis. Available here.
Central extensions and the classifying spaces of projective linear groups (2018). Preprint. Available at arXiv.

Software

mpfree, with Michael Kerber. Bitbucket.
Fast software for computing minimal presentations of 2-parameter persistence modules.
Persistable, with Luis Scoccola. GitHub.
Density-based clustering software with extensive visualization features.

Recorded talks

Some of my talks are available on YouTube:

Homology inference for the degree-Rips bifiltration. AATRN's Vietoris-Rips seminar.
The degree-Rips complexes of an annulus with outliers (1:01:20 mark). SoCG 2022.
Stable and consistent density-based clustering. ATMCS/AATRN 2020.

Contact information

Postal address:
Department of Mathematics, Technical University of Munich
Boltzmannstraße 3, 85747 Garching b. München, Germany

Email address: alexander dot rolle at tum dot de