Metric Embedding & Metric Geometry
Given the advances in the technology that permits the acquisition of massive amounts of data, and the consequent proliferation of large and complex datasets in different applied fields, computational methods for signaling/identifying meaningful patterns in such inputs are in high demand. The study of quantitative and computational aspects of metric spaces and their embeddings is featured prominently in the study of problems arising when analyzing such massive data endowed with a geometric representation. These problems include similarity search, visualization, clustering, and data compression. Analytic and computational results in Metric Geometry offer crucial insights into the solution of these problems. The theory of Metric Embeddings provides an interface between mathematics, and computer science, leading to powerful new algorithmic methods in the above contexts.