Open problems on classical de Sitter solutions
  Classical 10d string backgrounds with a 4d de Sitter space-time, D-brane and
orientifold sources, are commonly believed to satisfy the following:
  1. There is no classical de Sitter solution with parallel sources.
  2. Classical de Sitter solutions with intersecting sources are unstable.
  3. Classical de Sitter solutions cannot have at the same time a large
internal volume, a small string coupling, a bounded number of orientifolds and
quantized fluxes.
  These three conjectures are of particular relevance to the swampland program,
and if true, they challenge the connection of string theory to cosmology. We
restrict here to a standard solution ansatz for which the problem is
well-defined, and we still fail to prove analytically any of these conjectures.
While developing new tools and obtaining new constraints, we identify remaining
corners of parameter space where counter-examples to these conjectures could be
found.
