This conference is focused on Mathematical Logic, with connections to Theoretical Computer Science and the Philosophy/History of Set Theory. It will be an international meeting which will serve as the culmination of the Infinity Project, hosted at the CRM during 2009-2011. A unique feature of the Infinity Project and the proposed Conference is its explicit focus on interdisciplinarity in Mathematical Logic. 20 years ago the principal fields of Mathematical Logic (Set Theory, Model Theory, Proof Theory and Computation Theory) were closely related, but due to the subsequent dramatic developments in these fields, connections between them have been less common. Recent work however strongly suggests that time is now ripe for a concerted effort to forge deep new connections between these fields.