Unravelled Persistence
Inspired by the relative homology lattice and my previous work on the cohomological persistence theory of functions, I developed persunraveltorch, a library featuring a kernel, a method of vectorizing persistence intervals, and a type of group equivariant convolutional neural network layer.
Cohomological and Derived Persistence Theory of Functions
For most of my graduate studies I studied the persistence theory of functions through the lens of relative interlevel set cohomology (RISC). The results are consolidated in my thesis (submitted), which is a succession of the two preprints below (excluding Proposition 4.9 of arXiv:2108.09298).
Structure and Interleavings of Relative Interlevel Set Cohomology
- Coauthors
- Ulrich Bauer
- Magnus Bakke Botnan
Relative Interlevel Set Cohomology Categorifies Extended Persistence Diagrams
- Coauthors
- Ulrich Bauer
| Slides (displayed best in Chrome) | |
|---|---|
| January 27, 2023 | ARTIG #1 |
| December 13, 2022 | PSHT Seminar |
| August 18, 2022 | Biannual Austrian TDA Meeting |
| June 20, 2022 | ATMCS10 |
Universality of Distances on Invariants of Functions
As a part of my graduate studies I studied the universality of the bottleneck distance for extended persistence diagrams and the interleaving distance of merge trees.
Universal Distances for Extended Persistence
- Coauthors
- Ulrich Bauer
- Magnus Bakke Botnan
- Versions
- doi:10.1007/s41468-024-00184-7
- arXiv:2007.01834
Quasi-Universality of Reeb Graph Distances
- Coauthors
- Ulrich Bauer
- Håvard Bakke Bjerkevik
- Versions
- doi:10.4230/LIPIcs.SoCG.2022.14
- arXiv:2112.00720
Discontinued Notes on ...
... Interleaving Distances on Merge Trees
Revision 805091eade88 is the state that I submitted as the content of my master thesis under the supervision of Professor Rolf Klein. I am grateful for several useful discussions - often with his group - and the generous funding through the DFG project (KL 655/19) (D-A-CH).
- Formats
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- PDF (Letter)
- PDF A4
- LaTeX
- Source
- Internet Archive Snapshots
- 8 August 2017 - changeset: 726999dab694
- 8 September 2017 - changeset: c94ee4e01612
... Reeb Graphs and the Cohomological Cup Product in Degree Zero
- Formats
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- PDF (Letter)
- PDF A4
- LaTeX
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Posters
The Mayer-Vietoris Pyramid Sheaf-theoretically
Bridging Statistics and Sheaves- Abstract
- We provide a sheaf-theoretical version of the Mayer-Vietoris pyramid, introduced by Carlsson, de Silva, and Morozov, together with a notion of interleavings. We hope we can use this to gain an understanding how interleavings of levelset persistence introduced by Curry relate to interleavings of extended persistence introduced by Bubenik and Scott. Another hope is we can extend some of our ideas to situations where only partial information is available. Our constructions are heavily inspired by Happel's descriptions of the derived categories of Dynkin quivers and the Abelianization of triangulated categories.
Generic 1D-Interleavings
Spring School on Applied and Computational Algebraic Topology- Formats
- PDF (original poster) - changeset: 1cb388196827
- Revised PDF - changeset: 55d8607fbbc0
- Source