Mathematical Foundations of the Swampland Program

Recently, there has been great interest in determining criteria which differentiate between effective low-energy field theories which can be consistently completed in the ultraviolet into quantum gravity, said to be in the ‘Landscape’, from theories which appear consistent but nonetheless defy such a coupling to quantum gravity, the so-called ‘Swampland’. A number of such criteria, or Swampland Conjectures, have been proposed in the literature and attracted considerable interest in the high energy physics community. If confirmed, they have far-reaching consequences for physics and cosmology, such as for the structure of large field inflation in early time cosmology or for the mechanism responsible for the observed late-time acceleration of the universe, to name but the most striking ones. On the other hand, the Swampland Conjectures translate, in the context of string theory, into conjectures regarding the structure of possible compactifications, or string geometries. String theory is therefore in a unique position to quantitatively test - and possibly refine - such general Swampland Conjectures. This Scientific Program proposes to study these intriguing connections between general properties of quantum gravity and the geometry of string compactifications. It aims to bring together world experts working at the forefront of research in string theory, field theoretic aspects of quantum gravity, and geometry at this unique time in which our understanding of the Swampland is quickly evolving.