Abstract: 
Quantum position verification (QPV) is a cryptographic task in which the spatial location of an untrusted agent is certified using the principles of quantum mechanics and special relativity.  The problem of QPV has deep connections to computational complexity and the AdS/CFT correspondence.  In this talk I will introduce the task of QPV and describe how it fits under the general framework of information processing with spacetime constraints.  I will then turn to recent theoretical work analyzing the structure of QPV protocols in which the distribution of product states is used to certify a spatial location, and an honest prover must perform a joint measurement on the signals. This particular class of QPV protocols reveals separations in security based on whether the adversaries are restricted to classical versus quantum communication.  I will also use this as an opportunity to zoom out and describe other research topics of mine that are related to QPV.