# Related workshops and tutorials

- BIRS 5-day workshop on Topological data analysis and machine learning theory. Oct. 2012
- NIPS workshop on Algebraic Topology and Machine Learning. Dec. 2012
- ICML tutorial on Topological Data Analysis. June 2013
- IMA Thematic Year on Scientific and Engineering Applications of Algebraic Topology, Sept. 2013 -- June 2014
- SAMSI Workshop on Topological Data Analysis, Program on Low-dimensional Structure in High-dimensional Systems (LDHD) Feb. 2014

# Bibliography

- Douglas Arnold, Richard S. Falk, and Ragnar Winther, "Finite element exterior calculus: from Hodge theory to numerical stability," Bulletin of the American Mathematical Society, 47 (2010), no. 2, pp. 281- 354.
- Laurent Bartholdi, Thomas Schick, Nat Smale, and Steve Smale, "Hodge theory on metric spaces," Foundations of Computational Mathematics, 12 (2012), no. 1, pp. 1-48.
- Justin Bush, Marcio Gameiro, Shaun Harker, Hiroshi Kokubu, Konstantin Mischaikow, Ippei Obayashi, Pawel Pilarczyk, "Combinatorial-topological framework for the analysis of global dynamics, " Chaos, 22 (2012), 047508
- Ozan Candogan, Ishai Menache, Asu Ozdaglar, and Pablo Parrilo, "Flows and decompositions of games: harmonic and potential games," Mathematics of Operations Research, 36 (2011), no. 3, pp. 474-503.
- Ozan Candogan, Ishai Menache, Asu Ozdaglar, and Pablo Parrilo, "Dynamics in near-potential games,", Games and Economic Behavior, 82 (2013), pp. 66-90.
- Vin De Silva, "Point-cloud topology via harmonic forms," preprint, (2006), http://mmds.stanford. edu/slides/desilva-mmds.pdf.
- Vin de Silva, Dmitriy Morozov, and Mikael Vejdemo-Johansson, "Persistent cohomology and circular coordinates," Discrete and Computational Geometry, 45 (2011), no. 4, pp. 737-759.
- Tamal Dey, Anil Hirani, and Bala Krishnamoorthy, "Optimal homologous cycles, total unimodularity, and linear programming," SIAM Journal on Computing, 40 (2011), no. 4, pp. 1026-1044.
- Jozef Dodziuk, "Finite-difference approach to the Hodge theory of harmonic forms," American Journal of Mathematics, 98 (1976), no. 1, pp. 79-104.
- Jozef Dodziuk, "Combinatorial and continuous Hodge theories," Bulletin of the American Mathematical Society, 80 (1974), no. 5, pp. 1014-1016.
- Qiang Du, Max Gunzburger, Richard Lehoucq, and Kun Zhou, "A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws,", Mathematical Models and Methods in Applied Sciences, 23 (2013), no. 3, pp. 493-540.
- Joel Friedman, "Computing Betti numbers via combinatorial Laplacians," Algorithmica, 21 (1998), no. 4, pp. 331-346.
- R. Ghrist and Y. Hiraoka, "Network Codings and Sheaf Cohomology, " NOLTA 2011, 266-269.
- Anil Hirani, Kaushik Kalyanaraman, Han Wang, and Seth Watts, "Cohomologous harmonic cochains," preprint, (2011), http://arxiv.org/abs/1012.2835.
- Anil Hirani, Kaushik Kalyanaraman, and Seth Watts, "Least squares ranking on graphs," preprint, (2011), http://arxiv.org/abs/1011.1716.
- Alireza Tahbaz-Salehi and Ali Jadbabaie, "Distributed coverage verification in sensor networks without location information," IEEE Transactions on Automatic Control, 55 (2010), no. 8, pp. 1837-1849.
- Xiaoye Jiang, Lek-Heng Lim, Yuan Yao, and Yinyu Ye, "Statistical ranking and combinatorial Hodge theory," Mathematical Programming, 127 (2011), no. 1, pp. 203-244.
- Peter Kingston and Magnus Egerstedt, "Distributed-infrastructure multi-robot routing using a Helmholtz-Hodge decomposition," IEEE Conference on Decision and Control, Orlando, FL, Dececember 2011.
- Wenye Ma, Jean-Michel Morel, Stanley Osher, and Aichi Chien, "An L1-based variational model for retinex theory and its applications to medical images," Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (2011), pp. 153-160.
- Braxton Osting, Jerome Darbon, and Stanley Osher, "Statistical ranking using the l1-norm on graphs," Inverse Problems and Imaging, 7 (2013), no. 3, pp. 907-926.
- Donald Saari, Geometry of Voting, Springer-Verlag, Berlin, 1994.
- Amit Singer and Hau-tieng Wu, "Vector diffusion maps and the connection Laplacian," Communications on Pure and Applied Mathematics, 65 (2012), no. 8, pp. 1067-1144.
- Yiying Tong, Santiago Lombeyda, Anil Hirani, and Mathieu Desbrun, "Discrete multiscale vector field decomposition," ACM Transactions on Graphics, 22 (2003), no. 3, pp. 445-452.
- Qianqian Xu, Qingming Huang, Tingting Jiang, Bowei Yan, Yuan Yao, and Weisi Lin, "HodgeRank on random graphs for subjective video quality assessment," IEEE Transactions on Multimedia, 14 (2012), no. 3, pp. 844-857.
- Stella Yu, "Angular embedding: a robust quadratic criterion," IEEE Transactions on Pattern Analysis and Machine Intelligence, 34 (2012), no. 1, pp. 158-173.
- Xiaojin Zhu, "Persistent Homology: An Introduction and a New Text Representation for Natural Lan- guage Processing," The 23rd International Joint Conference on Artificial Intelligence (IJCAI), 2013.