Topological Methods in Data Analysis - Journal Club (Summer 2021)
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: Mondays 11h15 - 12h45
Zoom 830 4593 4507
Please get in touch with us to receive the password.
Organizers: Michael Bleher, Maximilian Schmahl, Daniel Spitz.
structures-hiwi@mathi.uni-heidelberg.de
Schedule
| Date | Topic | Info | Speaker | Slides |
|---|---|---|---|---|
| 12.04. | Introduction and Organization | Michael Bleher, Maximilian Schmahl | ||
| 19.04. | --- | --- | --- | |
| 26.04. | From Trees to Barcodes | Lida Kanari, Adélie Garin, Kathryn Hess (2020) |
Anja Randecker | |
| 03.05. | 3d Structure of DNA | Rabadan, R., & Blumberg, A. (2019). Topological Data Analysis for Genomics and Evolution: Topology in Biology. Cambridge University Press. doi:10.1017/9781316671665 |
Lukas Hahn | |
| 10.05. | Persistent homology analysis of phase transitions | Donato et. al (2020) Phys. Rev. E 93, 052138 https://journals.aps.org/pre/abstract/10.1103/PhysRevE.93.052138 |
Daniel Spitz | |
| 17.05. | Multi-Persistence | Maximilian Neumann (2021) https://arxiv.org/abs/2108.07632 |
Maximilian Neumann | |
| 24.05. | --- | --- Pfingsten --- | --- | |
| 31.05. | Stabilizing Functionals and Central Limit Theorems | Johannes Krebs | ||
| 07.06. | Topology identifies emerging adaptive mutations in SARS-CoV-2 | Michael Bleher, Lukas Hahn, Andreas Ott et al. (2021) https://arxiv.org/abs/2106.07292 |
Michael Bleher | |
| 14.06. | Probabilistic Convergence and Stability of Random Mapper Graphs | Brown, A., Bobrowski, O., Munch, E. et al. (2021) J Appl. and Comput. Topology 5, 99–140. https://doi.org/10.1007/s41468-020-00063-x |
Adam Brown | |
| 21.06. | Computing Image Persistence | Maximilian Schmahl | ||
| 28.06. | From Geometry to Topology: Inverse Theorems for Distributed Persistence | Elchanan Solomon, Alexander Wagner, Paul Bendich (2021) https://arxiv.org/abs/2101.12288 |
Freya Bretz | |
| 05.07. | ||||
| 12.07. | ||||
| 19.07. |
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.