강연자: Paweł Dłotko(University of Warsaw)

Title: On Clouds of Points and Their Shape: A Short Introduction to Topological Data Analysis

Abstract

Topological Data Analysis provides tools for studying the global structure of data: clusters, loops, holes, branches, and other geometric features that are often difficult to see using standard methods. In this lecture, we will give an informal and intuitive introduction to such tools as persistent homology, Mapper, Ball Mapper, and Euler characteristic curves and profiles.

The main idea is to look at data not only as a collection of numbers, but as an object with a shape. This shape may contain meaningful information that is not visible through averages, variances, or pairwise correlations alone. Topological features can help us explore complex datasets, compare different samples, build new descriptors, and support machine-learning models with interpretable geometric information.

The goal of the talk is to explain what we mean by the “shape of data,” how it can be measured, and why it may reveal important patterns in high-dimensional and complex datasets.

(공고요청: 이강주 박사)