Workshop Details

Distance Geometry (DG) is a classic mathematical field rooted in Heron's theorem and later generalized by Cayley and Menger. Some notable mathematical developments associated with DG are Euler's conjecture about the rigidity of polyhedra and Maxwell's work on force diagrams. Recent developments that have had considerable impact in applications are Schoenberg's theorem about the equivalence of distance matrices and positive semidefinite matrices and the Johnson-Lindenstrauss lemma, which is one of the cornerstones of the analysis of large-scale image databases. DG is particularly useful as an inference model for incomplete or noisy data, which makes it an important tool for data science. Engineering applications of DG have arisen in wireless networks, bioinformatics, robotics, control, architecture and many more. DG is also used in compressed sensing, low rank matrix completion, and the geometric representation of graphs. The breadth of its applicability enables DG to touch a wide range of disciplines. As an unfortunate consequence of such broad relevance, DG has developed in a fragmented way, resulting in rediscovery of ideas, duplication of terminology, and a lack of clear separation between fundamental theory and application details.

This workshop aims for unification in addition to scientific advancement. By inviting leading scientists in each application field and involving a large number of emerging researchers, we hope to move DG forward as a modern mathematical field with fundamental theoretical challenges and a rich supply of applications with potential for considerable societal impact. The workshop will: 1) highlight important mathematical and computational challenges in distance geometry; 2) draw connections to closely related mathematical problems in graph rigidity, semidefinite programming, matrix completion, among others; 3) involve leading researchers who are applying DG to applications in a wide range of fields; 4) involve a large group of students and early-career researchers; and 5) create new resources that we will use (and make available for others to use) to introduce newcomers to the concepts and applications of DG. The workshop will discuss the historical evolution of DG, identify common elements that appear in different applications, and encourage unification of terminology whenever possible. Several tutorials will be held during the workshop to facilitate such efforts.