TEW - Topology For Data Analysis (2026)
Speakers and Syllabus
| Name of the Speaker with affiliation | Lecture Hrs | Outline of the course |
| Chandan Maity (CM), IISER Berhampur |
3 Lectures | Fundamental group, covering space, Quotient space, Fundamental group of some quotient spaces. |
| Shameek Paul (SP) RKMVU, Belur |
4 Lectures | Finite Simplicial complexes. Polyhedra and Triangulations. Simplicial Approximation. Barycentric subdivision. Simplicial Homology. Lefschetz fixed point theorem. |
| Pralay Chatterjee (PC), IMSc, Chennai |
5 Lectures | Singular simplices, singular chain complexes. Exact sequence and Excision. Boundary maps and homology groups. Functoriality of singular homology. Comparison with simplicial homology for triangulable spaces. Mayer-Vietoris sequence and applications. Relative homology. |
| Krishnendu Gongopadhyay (KG), IISER, Mohali & Atish Mitra (AM) Montana Tech, USA |
6 Lectures | Motivation from topology of data: shape of data, noise versus signal. Simplicial complexes arising from data and filtrations as nested sequences of simplicial complexes. Persistent homology and persistence modules. Persistence diagrams and barcodes with examples and interpretations. Stability and basic applications of persistent homology in data analysis. Tutorial: Brief introduction to computational aspects and software tools such as GUDHI and Ripser. |
Tutor:
1. Kabir Kazi (KKa),IISER Mohali
2. Lokenath Kundu (LK), IISER Mohali
Suggested References.
1. Allen Hatcher, Algebraic Topology.
2. Glen E. Bredon, Topology and Geometry.
3. Gunnar Carlsson and Mikael Vejdemo-Johansson, Topological data analysis with applications, Cambridge University Press, Cambridge, 2022
Rationale for Including the Fourth Course
The first three courses of the workshop are devoted to foundational topics in algebraic topology, namely fundamental groups, simplicial complexes, and homology theories. The fourth course is included to demonstrate how these classical ideas lead naturally to modern developments in Topological Data Analysis (TDA).
Persistent homology is one of the most important contemporary applications of algebraic topology and has attracted significant interest in mathematics, data science, and computational research. Concepts such as simplicial complexes, filtrations, and homology groups introduced in the earlier lectures form the mathematical basis of persistent homology.
Thus, the fourth course serves as:
- A natural continuation of the earlier modules,
- An illustration of the applicability of algebraic topology in modern interdisciplinary research,
- And an introduction to an active area of current mathematical and computational interest.
- In the tutorial, some computational tools used in the subject will be introduced.
To improve thematic coherence, the module will emphasize the mathematical foundations of persistent homology and its connection with simplicial and singular homology, with only brief mention of omputational tools during the tutorial sessions. Since Topological Data Analysis is an emerging area at the interface of topology, computation, and data science, we believe that an introductory exposure to this subject will be valuable for college teachers and young researchers.
Time Table
| Day | Date | Lec 1 10:00–11:30 |
Tea 11:30–11:45 |
Lec 2 11:45- 13:15 |
Lunch 13.15- 15:00 |
Lec 3 15:.00-16:30 |
Tutorials & Discussions 16:30–17:30 |
| Mon | 28/12 | CM-1 | Tea | SP-1 | Lunch | PC-1 | LK+CM |
| Tue | 29/12 | CM-2 | Tea | SP-2 | Lunch | PC-2 | LK+PC |
| Wed | 30/12 | CM-3 | Tea | SP-3 | Lunch | PC-3 | LK+SP |
| Thurs | 31/12 | KG-1 | Tea | SP-4 | Lunch | PC-4 | KKa+KG |
| Fri | 01/01 | KG-2 | Tea | PC-5 | Lunch | AM-1 | KKa+AM |
| Sat | 02/01 | KG-3 | Tea | AM-2 | Lunch | AM-3 | Valedictory |