Recorded 27 March 2024. Jessica Purcell of Monash University presents "Constructing knots with specified geometric limits" at IPAM's Statistical Mechanics and Discrete Geometry Workshop. Abstract: Any infinite volume hyperbolic 3-manifold with finitely generated fundamental group that embeds in the 3-sphere is known to be a geometric limit of knot complements, but the original proof was only existential -- no knots were constructed. Using circle packings on the conformal boundaries of tame hyperbolic 3-manifolds, we give a constructive proof of this result -- except we can only guarantee our knots lie in the double of the original manifold, and not in the 3-sphere. Extending to the 3-sphere will require additional properties of circle packings. In this talk, I will discuss the construction and related open questions. This is joint work with Urs Fuchs and John Stewart. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-statistical-mechanics-and-discrete-geometry/