Explore the dynamical evolution of binary systems in star clusters and galaxies through this astrophysics seminar presented by Chris Hamilton from the Institute for Advanced Study. Delve into the complexities of orbital evolution in binary systems affected by external tidal forces, a fundamental problem in celestial mechanics. Discover recent advancements in the field, including the Lidov-Kozai theory, and examine various sources of tidal perturbations such as galactic gravitational fields, stochastic stellar encounters, and dark matter substructure. Learn about a general theory of tidally perturbed binaries and its applications to merging compact object binaries in stellar clusters. Gain insights into topics like the two-body and three-body problems, eccentricity, double black holes, and blue stragglers. Engage with a comprehensive discussion on the implications of this research for understanding exotic astrophysical phenomena, including LIGO/Virgo mergers of compact object binaries.