Topological Methods in Data Analysis - Journal Club (Summer 2020)
In recent years there has been a somewhat surprising flow of ideas from the mathematical branch of topology towards applications in the natural sciences. The tale of Topological Data Analysis (TDA) has it, that these methods provide a highly flexible, nonparametric approach to data analysis. Indeed, there are by now several well-known mathematical results that make statements of this kind rigorous. However, successful examples of TDA often build on a deep intuition about the system in question and many aspects of topological methods in data analysis remain a field of active research. The goal of this seminar is to offer a platform where we can learn about the TDA toolkit, discuss articles and new developments, and exchange ideas for the analysis of concrete datasets.
In case of questions, do not hesitate to contact us, the organizers of this Journal Club, via mail at structures-hiwi@mathi.uni-heidelberg.de.
Coordinates and Organization
Time: Tuesdays
even weeks: 16.15h to 17.45h
odd weeks: 17.00h to 18.00h(ish)
Location: Zoom meeting-ID: 830 4593 4507. Please get in touch with us to receive the password.
Organizers: Michael Bleher, Maximilian Schmahl, Daniel Spitz. Mail: structures-hiwi@mathi.uni-heidelberg.de.
Schedule
| Date | Topic | Info | Speaker | Slides |
|---|---|---|---|---|
| 21.04. | Test-run | This meeting will be dedicated to testing the technical setup with heiCONF and to discuss ideas for giving talks from home.
Feel free to join us - we would also be happy to use the opportunity and collect input from you! |
Daniel Spitz, Maximilian Schmahl & Michael Bleher | |
| 28.04. | Introduction and Organization | Maximilian Schmahl | Notes | |
| 05.05. 17h | Bauer: Ripser (Computing Barcodes for Persistent Homology Quickly) | https://arxiv.org/abs/1908.02518 | Maximilian Schmahl | Notes |
| 12.05. | Bardin, Spreemann, Hess: Topological exploration of artificial neuronal network dynamics | ArXiv: 1810.01747 | Aljosa | Slides |
| 19.05. 17h | Edelsbrunner, Wagner: Topological data analysis with Bregman divergences | ArXiv: 1607.06274 | Máté | |
| 26.05. | Chan, Carlsson & Rabadan: Topology of viral evolution | PNAS November 12, 2013 110 (46) 18566-18571 | Lukas | |
| 02.06. 17h | Bauer & Edelsbrunner: The Morse theory of Čech and Delaunay complexes | Trans. Amer. Math. Soc. 369 (2017), 3741-3762 | Daniel Spitz | Slides |
| 09.06. | Chen & Freedman: Hardness Results for Homology Localization | Discrete & Computational Geometry 45 (2011), 425-448 | Michael Bleher | |
| 16.06. | --- | --- | --- | |
| 23.06. | --- | --- | --- | |
| 30.06.
17h |
Usher, Zhang: Persistent homology and Floer-Novikov theory | https://arxiv.org/abs/1502.07928 | Levin | |
| 07.07. | Harrington, Otter, Schenk & Tilmann: Statifying multiparameter persistent homology | ArXiv: 1708.07390 | Carmen |
Further reading
For somewhat more details and introductory material on topological data analysis we refer to the literature section of this Wiki, which can be found here.