Geometric Constraint Systems

Explore the mathematical foundations and applications of geometric constraint systems through this comprehensive winter school program covering rigidity theory, distance geometry, matrix completion, tropical geometry, and graphical models. Delve into the rigidity of frameworks across three detailed lectures that establish core theoretical principles. Master distance geometry techniques and their applications in data science through multiple sessions examining computational methods and real-world implementations. Study matrix completion problems, chordal graphs, and semidefinite optimization techniques across three progressive lectures that connect algebraic and geometric approaches. Discover tropical geometry theory and applications through two foundational lectures introducing this emerging mathematical field. Investigate the geometric properties of triples of points in the plane through three specialized lectures exploring combinatorial and metric relationships. Examine graphical models from both combinatorial and geometric perspectives across three comprehensive sessions that bridge statistical modeling and geometric theory. Conclude by exploring the deep connections between graphical models and rigidity theory, synthesizing concepts from across the program to understand how these mathematical frameworks intersect and inform each other in modern applications.