Connectedness in Motion: Interactive Persistent Homology with Kotlin

Mathematically, we are fascinated by the shape hidden within data—how points connect, form clusters, and create holes. In this talk, I will show how we can bring these abstract ideas to life visually using Kotlin. By interactively adjusting the connectivity radius, we can watch points merge into components, loops appear, and topological features emerge and disappear. Using Multik for computations, Kotlin DataFrame for handling CSV data, Kotlin Statistics for analysis, and Jetpack Compose for interactive visualizations, we can see the mathematics of connectedness unfold in real time. This talk focuses not just on the data itself but on the story of its shape, making topology tangible and interactive on mobile devices.

Understand how topological concepts such as connected components and loops reveal the underlying shape of data. Learn how changing a connectivity radius affects data structure and why features appear and disappear. Gain practical experience using Kotlin for mathematical and data-driven applications, beyond traditional Android use cases. See how Multik can be applied to numerical and matrix-based computations in real-world scenarios. Learn to handle and explore datasets using Kotlin DataFrame and Kotlin Statistics Discover how Jetpack Compose enables interactive, real-time data visualizations on mobile devices. Develop intuition for topological data analysis (TDA) through visual and interactive exploration rather than abstract theory alone. Take away patterns for building interactive scientific visualizations in Kotlin-based applications.