AdS/CFT, self-adjoint extension and the resolution of cosmological singularities

In the context of Einstein gravity coupled to matter satisfying fairly general energy conditions, cosmological singularities are unavoidable, as was proven by Hawking and Penrose many year ago. One of the hopes for superstring theory is that a solution to this problem may be found. Clearly, however, a non-perturbative formulation of string theory must be used. The AdS/CFT correspondence is a proposed definition of non-perturbative string theory (including gravity) in terms of a conformal field theory which does not involve gravity. It has been conjectured that the AdS/CFT correspondence can be used to resolve cosmological singularities. Initial work in this direction was done by different groups, including Craps-Hertog-Turok, Khoury-Ovrut-Steinhardt-Turok, Skenderis-McFadden, Silverstein-Horowitz and Das-Tridevi.

This workshop will bring together pure mathematicians, string theorists and cosmologists to tackle the problem of singularity resolution via the AdS/CFT correspondence. From the point of view of cosmology it will be important to include cosmological perturbations (fluctuations which could describe the currently observed structure of the inhomogeneous universe). Thus, the mathematics of the problem will involve the theory of partial differential equations and self-adjoint extensions. A close interaction of physicists and mathematicians is required to make progress on the problem.