Workshop on Distance Geometry - Semidefinite Programming and Applications

Explore advanced mathematical concepts through this comprehensive workshop covering distance geometry, semidefinite programming, and their diverse applications across multiple domains. Delve into polynomial optimization techniques including sums of squares and moment methods, examine distance matrix completions and classical Toeplitz matrices, and investigate random projections for conic programs. Study the structural properties of Euclidean distance matrix (EDM) cones and their intersections with linear subspaces, while analyzing performance metrics for polynomial optimization hierarchies. Examine rigidity theory through universal rigidity of generic symmetric tensegrities and global rigidity of unit ball graphs, and explore semidefinite programming bounds for geometric problems like the average kissing number. Investigate k-diametral point configurations in Minkowski spaces, connections between sums of squares of polynomials and graph theory, and orthogonality properties of isometries in conformal models. Learn about asymptotic behaviors of eigenfrequencies in Maxwell equations with small deformations, determinant calculations for stress matrices in pinned frameworks, and practical applications including distance geometry for word embeddings, source localization with strong convexity properties, and target tracking using time-of-arrival methods. Understand the emergence of exponential size solutions in semidefinite programming and gain insights into cutting-edge research at the intersection of optimization, geometry, and computational mathematics.