 Herbert Edelsbrunner

Herbert Edelsbrunner develops algorithms for computational geometry and computational topology. His research account describes a progression from data structures and geometry to topological methods, guided by applications.^[ref] He coauthored Computational Topology: An Introduction by Herbert Edelsbrunner and John L. Harer with John L. Harer.^[ref]

A central computational challenge is to replace a continuous shape by finite combinatorial data while preserving the invariant being studied. For example, a triangulated surface can be described by vertices, edges and faces, allowing homology to be computed from boundary relations. The representation supplies an algorithmic route to a geometric question; the quality of the input model remains part of interpreting the answer.