In the past five years their have a been number of significant advances in the mathematics of QFT on manifolds with boundary. The work of Cattaneo, Mnev, and Reshitihkin--beyond setting rigorous foundations--has led to many computable and salient examples. Similarly, the work of Costello (specifically projects joint with Gwilliam and Si Li) provides a framework (and deformation/obstruction) for the observable theory of such theories with boundary/defects. There are related mathematical advances: constructible factorization algebras and higher category theory as pioneered by Lurie and the collaboration of Ayala, Francis, and Tanaka. The goal of the workshop is to bring together the leading experts in this multi-faceted subject.The structure of the workshop will be such as to maximize the exchange of knowledge and collaboration. More specifically, the morning sessions will consist of several lecture series, while the afternoons will be reserved for research working groups. The mornings will communicate the essential ideas and techniques surrounding bulk-boundary correspondences and perturbative AKSZ theories on manifolds with boundary/corners. The afternoons will be research driven and focus on specific problems within the following realms: the interaction of renormalization with cutting/pasting, aspects of the AdS/CFT correspondence, cohomological approaches to gravity, and the observable/defect theory of AKSZ type theories.