- clustering algorithms and Reeb graph / dendrogram reconstruction
- computational topology
- surface/manifold reconstruction and mesh generation
- computing optimal homology generators
- metric measure spaces and shape matching
- low-distortion metric embeddings
- Morse theory
- random graphs and percolation theory
- random topology
- shape analysis
- topological graph theory
- geometric approximation algorithms
- persistent homology and cohomology, and applications
- spectral and geometric methods in machine learning and data analysis
- geometric and topological methods in data analysis

- Misha Belkin. CSE and Stats.
- Dan Burghelea. Math.
- Mike Davis. Math.
- Tamal Dey. CSE.
- Roy Joshua. Math.
- Matthew Kahle. Math.
- Sanjeevi Krishnan. Math.
- Sebastian Kurtek. Stats.
- Facundo Memoli. Math and CSE.
- Anastasios Sidiropoulos. CSE and Math.
- David Sivakoff. Stats and Math.
- Rephael Wenger. CSE.
- Yusu Wang. CSE.

- Mini-course by Patrizio Frosini -- Some new results in two-dimensional and group-invariant persistent homology. (3--7 April, 2017).
- Sheaf Theory. Spring 2017. Sanjeevi Krishnan.
- Computational Topology and Data Analysis. Spring 2017. Tamal Dey.
- Applied Algebraic Topology. . Fall 2016. Crichton Ogle and Facundo Mémoli.
- Topics on Networks Data Analysis. Spring 2016. Facundo Mémoli.
- Computational topology: Theory, algorithms and applications to data . Spring 2016. Yusu Wang.
- Mini-course by Jose Perea -- Some Applications of Algebraic Topology to the Analysis of Data. (16--20 November, 2015).
- Reading Group on Applied Algebraic Topology. (Autumn 2015) Roy Joshua, Facundo Mémoli and Crichton Ogle.
- Mini-course by Justin Curry -- Sheaves, Cosheaves, and Applications. (9--13 March, 2015).
- Reading Group on Applied Algebraic Topology. (Spring 2015) Crichton Ogle and Facundo Memoli.
- Random Spaces and Random groups. (Spring 2015) Matthew Kahle.
- Computational Topology and Data Analysis. Tamal Dey
- Random graphs and percolation. Matthew Kahle.
- Metric geometry in data analysis. Facundo Memoli.
- Algorithm design under a geometric lens. Tasos Sidiropoulos.
- Introduction to Computational Topology: an algorithmic view. Yusu Wang.

- DowkerPH. Persistent Homology of Asymmetric Networks.
- AYLA. Collaborative visual analytic platform. Produces a 2D-terrain metaphor to visualize/explore the high-dimensional molecular simulation data.
- CoCone. Surface reconstruction software.
- DENALI. Tool to visualize scalar functions defined on trees, graphs and point clouds using a terrain metaphor.
- HanTun.Software for Computing Handle and Tunnel Loops in 3D Models.
- ShortLoop. Soft for computing shortest homology basis.

- Applied Algebraic Topology network.
- ACAT, Applied and Computational Algebraic Topology, ESF network.
- Computational Topology Group at Stanford.