Part 1: April 24 - May 6, 2017
Part 2: September 4 - 29, 2017
Organizers: Herbert Edelsbrunner, Michael Farber, Dmitry Feichtner-Kozlov, Kathryn Hess, Martin Raussen
Description: Scientific and engineering disciplines are in increasing need of effective methods for distilling and analyzing structural information from vast quantities of complex data. In recent years, ideas and methods from algebraic topology, combined with the development of fast algorithms and user-friendly software, have proven valuable in this endeavor. This program aims at stimulating and enhancing collaboration between experts in several areas of applied and computational topology, together with scientists actively working on problems the solution of which might require topological insights and machinery. It will focus on the following three areas of investigation:
- Topological and statistical analysis of shapes, images, and multi-dimensional data sets
- Stochastic topology
- Topological contributions to the theory of concurrent computation and computer networks
Associated Events: The program comprises two parts:
- A spring school and an international interdisciplinary conference (April 24 - May 6, 2017)
- Collaboration between experts in applied and computational algebraic topology, both senior and junior, including focused seminars (September 4 - 29, 2017)
No. |
Author(s) |
Title |
Preprint |
Publication |
| 2017c01 | Grigoriev, Dima; Vorobjov, Nicolai | Upper bounds on Betti numbers of tropical prevarieties | 1709.08594 | MR3810572 |
| 2017c02 | Batko, Bogdan; Kaczynski, T.; Mrozek, M.; Wanner, T. | Linking combinatorial and classical dynamics: conley index and morse decompositions | 1710.05802 | |
| 2017c03 | Bauer, Ulrich; Bjerkevik, H.K. | Tight equivalences of metrics between Reeb graphs | in preparation | |
| 2017c04 | Belton, Robin; Brooks, R.; Ebli, L.; Fajstrup, Lisbeth; Fasy, Brittany; Ray, C.; Sanderson N.; Vidaurre, E. | An obstruction to contractibility of spaces of directed paths | 1902.01039 | |
| 2017c05 | Bjerkevik, Havard; Botnan, Magnus | Computational complexity of the interleaving distance | MR3824257 | |
| 2017c06 | Bjerkevik, Havard; Botnan, Magnus; Kerber, Michael | Computing the interleaving distance is NPhard, 2018 | 1811.09165 | |
| 2017c07 | Brodzki, Jacek; Gao, T.; Mukherjee, S. | The geometry of synchronization problems and learning group actions | 1610.09051 | Discrete Comput. Geom. (2019) |
| 2017c08 | Bubenik, Peter | The persistence landscape and some of its properties | 1810.04963 | Proceedings of the 2018 Abel Symposium (accepted) (2019) |
| 2017c09 | Bubenik, Peter; Hull, Michael; Patel, Dhruv; Whittle, Benjamin | Persistent homology detects curvature, 2019 | 1905.13196 | |
| 2017c10 | Bubenik, Peter; Vergili, T. | Topological spaces of persistence modules and their properties | 1802.08117 | MR3927353 |
| 2017c11 | Chacholski, Wojciech; Levi, Ran; Meshulam, Roy | On the topology of complexes of injective words | 1908.03394 | submitted |
| 2017c12 | Chen, Chao; Ni, X.; Bai, Q.; Wang, Yusu | A topological regularizer for classifiers via persistent homology | 1806.10714 | Proceedings of Machine Learning Research (K. Chaudhuri and M. Sugiyama, eds.)Proceedings of Machine Learning Research, vol. 89, PMLR, 16–18 Apr 2019, pp. 2573–2582. |
| 2017c13 | Dey, Tamal; Juda, Mateusz; Kapela, T.; Kubica, J.;Lipinski, M.;Mrozek, Marian | Persistent homology of Morse decompositions in combinatorial dynamics | 1801.06590 | MR3922908 |
| 2017c14 | Goubault, Eric | On directed homotopy equivalences and a notion of directed topological complexity | 1709.05702 | |
| 2017c15 | Goubault, Eric; Farber, Michael; Sagnier, Aurélien | Directed topological complexity | 1812.09382 | |
| 2017c16 | Grigoriev, Dima; Vorobjov, Nicolai | Orthogonal tropical linear prevarieties | 1803.01068 | MR3854801 |
| 2017c17 | Kaczynski, Tomasz; Mrozek, Marian; Wanner, Thomas | Creating semiflows on simplicial complexes from combinatorial vector fields | in preparation | |
| 2017c18 | Kozlov, Dmitry; Meshulam, Roy | Quantitative aspects of acyclicity | 1802.03210 | MR4011565 |
| 2017c19 | Kurlin, Vitaliy; Muszynski, Grzegorz | A persistence-based approach to automatic detection of line segments in Images | International Workshop on Computational Topology in Image Context (R. Marfil, M. Calderon, Diaz del Rio F., P. Real, and A. Bandera, eds.), L, vol. 11382, Springer, 2019, pp. 137–150 | |
| 2017c20 | Lütgehetmann, Daniel; Govc, Dejan; Smith, Jason; Levi, Ran | Computing persistent homology of directed flag complexes | 1906.10458 | |
| 2017c21 | Patrangenaru, V.; Bubenik, Peter; Paige, R. L.; Osborne, D. | Challenges in topological object data analysis | MR3982197 | |
| 2017c22 | Raussen, Martin | Pair component categories for directed spaces | 1812.09507v2 | |
| 2017c23 | Raussen, Martin | Inessential directed maps and directed homotopy equivalences | 1906.09031 | |
| 2017c24 | Rieser, Antonio | Cech closure spaces: A framework for discrete homotopy | 1708.09558v5 | |
| 2017c25 | Rybakken, Erik; Baas, Nils A.; Dunn, B. | Decoding of neural data using cohomological feature extraction | MR3898980 | |
| 2017c26 | Spreemann, Gard; Dunn, B.; Botnan, Magnus; Baas, Nils A. | Using persistent homology to reveal hidden covariates in systems governed by the kinetic ising model | MR3789145 | |
| 2017c27 | Zhang, K.; Wu, P.; Yuan, Ch.; Wang, Yusu; Metaxas, D.; Chen, Chao | Heuristic search for homology localization problem and its application in cardiac trabeculae reconstruction | accepted at 28th International Joint Conference on Artificial Intelligence (IJCAI), 2019 | |
| 2017c28 | Ziemianski, Krzysztof | Spaces of directed paths on pre-cubical sets II | 1901.05206 | |
| 2017c29 | Ziemianski, Krzysztof | Stable components of directed spaces | 1805.05061 | MR3942260 |
Those planning to participate include:
Gerard Ben Arous, Ginestra Bianconi, Peter Bubenik, Gunnar Carlsson, Frédéric Chazal, Lisbeth Fajstrup, Maurice Herlihy, Yasuaki Hiraoka, Matthew Kahle, Roy Meshulam, Konstantin Mischaikow, Dmitriy Morozov, Marian Mrozek, Michel Raynal, Sergio Rajsbaum, Primoz Skraba, Vanessa Robins, Ulrike Tillmann, Yusu Wang, Shmuel Weinberger
