OneMath World School 2026

Topological Data Analysis and Applications

A Practical Workshop on TDA Methods and Applications

February 20-28, 2026

FC Kohli Center, CMI, SIPCOT IT Park

About the School

The OneMath World School is a first-of-its-kind global program initiated by BIRS partner institutions. It is designed to connect young mathematical talent with leading experts in emerging fields. This initiative brings together advanced undergraduates, graduate students, and early-career researchers from around the world to collaborate with established leaders and explore cutting-edge topics at the intersection of theory and application. Visit the link for more details.

This School provides a practical introduction to topological data analysis (TDA) with emphasis on hands-on techniques and implementation. Participants will learn to apply TDA methods, particularly Persistent Homology and the Mapper algorithm, to extract meaningful features from complex datasets.

Target Audience

Masters and PhD students, postdocs, and early career researchers in Mathematics and Computer Science

Participants

Up to 40 participants with 8 local and invited speakers

Prerequisites

Participants should have proficiency in either:

  • Basic algebraic topology, OR
  • Machine learning fundamentals and Python programming
Important Dates
  • Registration Deadline
    December 15, 2025
  • Selection Announcement
    December 31, 2025
  • Boot Camp
    February 20-21, 2026
  • Mini Courses
    February 23-26, 2026
  • Group Projects
    February 27-28, 2026

Program Structure

Day 1-2 Boot Camp

February 20-21, 2026

A comprehensive introduction to bring all participants to the same foundational level:

  • Crash course on simplicial complexes and combinatorial techniques
  • Simplicial homology and related linear algebra
  • Machine learning fundamentals: classification algorithms, clustering and dimensionality reduction
  • Python tutorials for ML implementation

Day 3-6 Mini Courses

February 23-26, 2026

Four days of intensive lectures and hands-on tutorials:

  • Morning sessions: Theoretical foundations and advanced concepts
  • Afternoon sessions: Hands-on tutorials with Python libraries

Day 7-8 Group Projects

February 27-28, 2026

Participants work in groups on real-life applications:

  • Image analysis: classification, segmentation, boundary detection
  • Time series and signal processing
  • Robotics applications

Mini Courses

Introduction to Persistent Homology
  • Filtrations of topological spaces
  • Simplicial complexes from point clouds
  • Persistent barcodes and diagrams
  • scikit-tda library
  • Stability and distances
Mapper Algorithm
  • Morse theory and Reeb graphs
  • Topological Mapper construction
  • Parameter selection techniques
Topological Machine Learning
  • Persistence landscapes and other vectorization methods
  • Euler characteristic transforms
  • Feature engineering for ML
Applied Persistent Homology
  • Configuration space of the cyclo-octane molecule
  • Anisotropic Kuramoto-Sivashinsky equation
  • Time series analysis and Takens' embedding theorem
Topology in Visualization
  • Visualization of scientific data
  • Applications of Mapper
  • KeplerMapper library

Invited Speakers

Henry Adams

University of Florida

Vijay Natarajan

IISc Bangalore

Steve Oudot

Inria Saclay - Ile-de-France

Bastian Rieck (Online)

University of Fribourg

Bei Wang (Online)

University of Utah

D. Yogeshwaran

ISI Bangalore

More speakers TBA

Additional speakers to be announced

Schedule

All times are tentative and will be updated as speakers confirm.
Venue : LH 202 (2nd floor, multistory building)

Time Title / Topic Speaker Notes
20 Feb 2026
09:30–11:00 Intro to machine Learning Madhavan Mukund slides
11:30–13:00 Applied topology Priyavrat Deshpande slides
14:00–15:15 Python session TBA
15:45–17:00 Tutorial session TBA
21 Feb 2026
09:30–11:00 Into to machine learning Madhavan Mukund slides
11:30–13:00 Algorithmic topology and discrete Morse theory Siddharth Pritam slides
14:00–15:15 Python session TBA
15:45–17:00 Tutorial session TBA
Time Title / Topic Speaker Notes
23 Feb 2026
09:30–11:00 Intro to persistent homology Steve Oudot slides
11:30–13:00 Applied persistent homology Henry Adams slides
14:00–15:15 Tutorial session TBA
15:45–17:00 Tutorial session TBA
24 Feb 2026
09:30–11:00 Into to persistent homology Steve Oudot slides
11:30–13:00 Applied persistent homology Henry Adams slides
14:00–15:15 Tutorial session TBA
15:45–17:00 Tutorial session TBA
25 Feb 2026
09:30–11:00 Topology in Visualization Bei Wang slides, tutorial, datasets
11:30–13:00 Intro to Reeb graphs Vijay Natarajan slides
14:00–15:15 Topological machine learning Bastian Rieck slides
15:45–17:00 Tutorial session TBA
26 Feb 2026
09:30–11:00 Topology in visualization Bei Wang slides, tutorial, datasets
11:30–13:00 Intro to Reeb graphs Vijay Natarajan slides
14:00–15:15 Topological machine learning Bastian Rieckn slides
15:45–17:00 Tutorial session TBA
Time Title / Topic Speaker Notes
27 Feb 2026
09:30–11:00 Topology of random point samples D. Yogeshwaran
11:30–13:00 Group work
14:00–15:15 Group work
15:45–17:00 Group work
28 Feb 2026
09:30–11:00 Group Work
11:30–13:00 Group work
14:00–15:15 Group work
15:45–17:00 Group work
Jupyter Notebooks

These hands-on notebooks are designed to complement the boot camp and mini-course sessions. They walk you through the implemetation of some ML algorithms, computing persistent homology, and visualizing barcodes and persistence diagrams using standard Python libraries including Giotto-TDA, ripser, Kepler Mapper, and scikit-learn. No prior TDA coding experience is assumed — the notebooks are self-contained and progress from elementary examples to more advanced pipelines.

View on GitHub
Group Projects

The following projects are curated to give participants meaningful exposure to real-world applications of TDA. Each project in the first list comes with several relevant papers, suggested dataset, guiding questions. Participants are encouraged to pick a project based on their background and interests, and to bring their own data if they have a problem in mind.

View Projects
Topology of random point samples (abstract): We will look at topology of random point samples on a flat torus or Euclidean space. From these samples we build geometric complexes—most notably the Čech complex—and ask what can be inferred about the topology of the underlying space. These are illustrative of the more general question of inferring topology of a manifold from random point samples on a manifold. Two central phenomena are emphasized. First, homological phase transitions, sharp thresholds in the connectivity radius at which homological features (captured by Betti numbers) emerge and vanish with high probability. Second, limit theorems for homological invariants, including laws of large numbers and central limit theorems governing the asymptotic behavior of (Persistent) Betti numbers across scaling regimes. Basic knowledge of homology theory and probability will be assumed.

Registration

Registration for the School is over. Confirmed participants have already been notified.

Local Organizers

Priyavrat Deshpande

Chennai Mathematical Institute

Vijay Natarajan

IISc Bangalore

Siddharth Pritam

Chennai Mathematical Institute