Explore the intricacies of cylindrical contact homology in this advanced mathematics seminar presented by Jo Nelson from Rice University. Delve into the evolution of contact geometry, examining the existence of periodic orbits and the machinery invented to study them. Investigate the concept of regularity in domain-dependent J, the introduction of point constraints, and the emergence of cascade moduli spaces. Analyze the development of a new chain complex and the rise of obstruction bundles. Conclude with an in-depth look at obstruction bundle gluing setup and the resulting gluing obstruction, gaining valuable insights into this complex area of symplectic geometry.