Duality symmetries, higher derivatives, and their applications in cosmology
The goal is to uncover symmetries and dualities of string theory including \alpha' corrections, to describe massive string states, and to investigate applications in cosmology. This will be done using double field theory and exceptional field theory and generalizing it to the non-local interactions of genuine stringy states and/or an infinite number of higher-derivative \alpha' corrections. So far these frameworks were mainly used to describe the low-energy effective field theories of the massless states in string/M-theory in a manifestly duality invariant way. The anticipated generalizations require a significant deformation or extension, of which we have only recently obtained first glimpses. 

Specifically, the higher-derivative corrections are constrained by gauge symmetries. These include the Green-Schwarz transformations, but are far more general and determine all corrections to first order in \alpha'. There was also recent progress on the problem of including massive string states: Sen proved that the sub-sector of string theory consisting of massless fields together with their Kaluza-Klein and winding modes provides a consistent truncation. The resulting theory must be governed by L_{\infty} algebras, which are generalizations of Lie algebras that so far have played little role in conventional field theories but now give us a concrete clue of how to construct a `true double field theory'. 

Various string cosmology scenarios have been suggested that aim to utilize stringy features for, say, the early universe. 
However, given our ignorance about the precise `stringy' Einstein equations, it has been impossible to test and verify such ideas, even theoretically. In view of the recent and forthcoming PLANCK data it has become particularly urgent to find a useful formulation of string theory in which problems of this type can be addressed and analyzed. If successful, this research program would be ground-breaking in that it would allow us to do precisely this.