Distance geometry is a research area bridging mathematics and computer science with applicability to practical problems in a wide range of disciplines. In the majority of the applications, we are given an incomplete list of distances between pairs of objects, and we seek positions in Euclidean space realizing those distances. Classical applications include topics as protein conformation determination and sensor network localization, while emerging applications range from the study of molecular nanostructure to the adaptation of human movements in simulated environments. Distance geometry is also used in important data science applications such as compressed sensing, low rank matrix completion, and visualization of high-dimensional data.
 
Semidefinite programming has been exploited in the solution of many of these problems concerning Euclidean distance, as for example, to construct relaxations for the problems of sensor network localization, metric-space embedding and Euclidean distance matrix completion. Among other important distance geometry applications with connections to semidefinite programming, we highlight the universal and dimensional rigidity and pre-stress stability, which admit close links to semidefinite programming and gram matrices, including connections to low rank matrix completion.  Furthermore, the study of coordinate shadows, projections and fibers of the dimensional strata of  Euclidean and L_p distance cones provides bridges both to geometric analysis and to algebraic geometry and configuration spaces.

Specifically, they are used in  configuration space  descriptions using Cayley or distance parameters and a notion called flattenability that is related to generic rigidity and graph forbidden minors.

This workshop aims at highlighting important mathematical and computational challenges in distance geometry, at setting connections to related semidefinite programming problems, and at discussing applications of distance geometry in diverse areas, by gathering leading researchers in the field.

All times are in Toronto local time (Eastern Time)