Conference Service Mandl

abstract: The aim of this permanent school is to introduce undergraduate and Ph.D. students in Mathematics and Physics as well as post-doctoral researchers in a recently emerged area of Mathematics and Theoretical Physics: Secondary Calculus. A 'diffiety' is a new geometrical object that properly formalizes the concept of the solution space of a given system of (nonlinear) PDEs, much as an algebraic variety does with respect to solutions of a given system of algebraic equations. Secondary Calculus is a natural diffiety analogue of the standard Calculus on smooth manifolds, and as such leads to a very rich general theory of nonlinear PDEs. It appears that it is this the only natural language of quantum physics, just as the standard Calculus is for classical physics.

abstract: An exciting and largely unexpected consequence of Holography is that String and M-theory can provide useful information for transport phenomena of strongly interacting theories in low dimensions, fluid mechanics and non-relativistic systems. Physical systems that may have dual holographic descriptions include quantum critical points in 2+1 dimensions, high-Tc superconductors, quantum Hall systems, systems that exhibit parity breaking, non-relativistic critical systems as well as fluid mechanics and turbulence. Such systems – the Holographic States of Matter - have the potential to radically alter the perception of string theory and its relevance for physics. A basic theoretic setup for the holographic study of such systems is AdS4/CFT3 correspondence. This is also the main framework for holographic studies of the mysterious M-theory. The subject has experienced great formal growth, driven by the discovery of various field theoretical models for M2-branes. It is a fortunate and intriguing that progress in the more applied directions coincides with enhancement in the understanding of more formal aspects of M-theory. By bringing together experts in both the applied and formal directions we aim to create a fertile environment where future developments regarding the Holographic States of Matter in connection with our understanding of M-theory can be studied.