String compactifications have mostly focussed on geometrical constructions. Prime examples that preserve a certain amount of target space supersymmetry are Calabi-Yau and
orbifold compactifications. However, it has been realized very early on that string theory also admits constructions that do not admit any (easy) geometrical interpretation, for
example asymmetric orbifolds, free-fermions and Gepner models.
Recently the field of non-geometrical string compactifications has revived. One motivation for this has been the search for constructions that provide a build-in mechanism for moduli
stabilization. Another reason is that it has been realized that maximal (N=8) supergravities in four dimensions admit many gaugings, but only a small subset of those can be associated
with compactifications of 10D supergravity. Some of the other gauge supergravities can be obtained by applying T-dualities to the geometrical compactifications. Hence, one expects
that there must be some sort of lift of these 4D gauged supergravities to 10D string theory. They go under the name of non-geometrical flux backgrounds.
Since an underlying idea is that various configurations of fluxes are related by T-dualities, it would be useful to have a formulation of the low-energy theory of string theory that
is T-duality covariant. Here, double field theory enters the scene: it is a construction in which the number of coordinates are doubled to make T-duality manifest.
Double field theory is one attempt to have a definite stringy description of non-geometry. Another approach is to use asymmetric orbifolds. Even though these orbifolds do not have a
simple geometrical interpretation, they provide exactly solvable string solutions. The connection between them and the non-geometric fluxes has recently been investigated. In addition
some first attempts have been made to do model building on such backgrounds. Furthermore, a natural description of asymmetric Z2xZ2 orbifolds are free-fermionic constructions. Also,
quite recently, there has been a full classification of all symmetric orbifold geometries compatible with heterotic N=1 or more supersymmetry in four dimensions using the language of
cristallography. It would therefore be very interesting to obtain a similar classification of asymmetric orbifolds. In addition the techniques to determine the nature of the
non-geometrical fluxes might also be applicable to more involved non-geometrical string constructions like Gepner models.
In this workshop we wanted to bring together experts on the various aspects of non-geometry and exact string constructions to share their recent results and discuss how some of the
open questions mentioned above can be addressed.
The homepage of the program is available here