Over the last few years there has been a growth in developing new geometric concepts associated to ideas coming from string and M-theory. These have included: generalised geometry; double field theory; U-duality manifest formulations of M-theory; extended exceptional geometries; and much more. These developments initially had various motivations including: making duality symmetries manifest in some framework; combining p-form gauge transformations with diffeomorphisms to produce a novel algebraic structure and other ideas concerning making a geometric formulation of gravity and p-form fields together. The key to these developments has been to extend the number of dimensions of spacetime to include novel directions that correspond to winding modes of strings or branes. The developments over the last few years have concentrated on developing the formalism in terms of the production of actions; identifying local symmetries and understanding how to project down from the higher dimensional theory to the usual spacetime description. By now the connection to ordinary supergravity and gauged supergravities in lower dimensions through the embedding formalism is quite well understood.

There are however several key questions that remain and the field is very active. Also, given the extensive development of the formalism, it is now the time to start applying it to problems of interest, in particular to questions concerning compactifications, black holes and fundamental mathematical structures.

**Organizers**: David Berman, Martin Cederwall, Nakwoo Kim, Sang Min Lee, Wolfgang Lerche, Jeong-Hyuck Park, Hagen Triendl

**Topics:**

- the possibility of producing and rigorously investigating genuinely non-geometric backgrounds in double field theory and M-theory equivalents as generalised geometric backgrounds;
- the physical interpretation of DFT in the absence of isometries and localisation in winding space;
- the geometric description of the so called “exotic branes” of deBoer and Shigemori;
- a tool for understanding mirror symmetry;
- the various mathematical structures behind extended and double geometry such as possible non-associative structures;
- new phenomenological implications of non-geometric compactifications;
- the study of cosmological backgrounds
- the understanding of a genuine CFT description of DFT;
- quantum aspects of these theories;
- application of these ideas to black hole physics, thermodynamics and singularity structure;
- what is the global structure of the exceptional geometries both in terms of finite gauge transformations and in terms of a geometric patching to give global solutions.

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