Computational Topology

Computational topology is a branch of mathematics that focuses on understanding the shape and structure of data through algorithms. It allows researchers to analyze complex geometrical and topological features of objects, often by representing them as simpler forms. This has practical applications in various fields, including computer graphics, data analysis, and even biology, where we can study shapes of proteins or shape patterns in data sets. By using tools from both computer science and topology, it aims to uncover hidden patterns and relationships in high-dimensional spaces and to make sense of complex datasets.