In this talk, we examine a fundamental question posed some time ago by Birkhoff and von Neumann: What are the possible structures of measurement in a theory of Physics? We find striking connections with the conceptual framework of First Order Logic, and apply classification theorems for the automorphism groups of first order relational structures to argue for the uniqueness of Hilbert space as the phase space of a theory with probabilistic transitions between atomic states. We discuss possible applications of these observations to Algebraic Quantum Field Theory.

I will discuss the newly discovered Y(p,q) quiver gauge theories, which are dual to Type IIB string theory on AdS5 x Y(p,q). The metrics on the five-dimensional Y(p,q) manifolds are explicitly known, thus opening up exciting possibilities. Special emphasis will be placed on the toric phases of these theories and their Seiberg duality structure.