[for zoom details please email s.nagy@qmul.ac.uk] In this talk we discuss a new swampland conjecture stating that the limit of vanishing gravitino mass corresponds to the massless limit of an infinite tower of states and to the consequent breakdown of the effective field theory. The proposal can be tested in large classes of models coming from compactification of string theory to four dimensions, where we identify the Kaluza-Klein nature of the tower of states becoming light. We point out a general relation between the gravitino mass and an abelian gauge coupling, which allows us to connect our conjecture to the weak gravity conjecture or the absence of global symmetries in quantum gravity. We discuss phenomenological implications of our conjecture in (quasi-)de Sitter backgrounds and extract a lower bound for the gravitino mass in terms of the Hubble parameter.

In this talk we discuss the geometric and non-geometric faces of closed string vacua. The associated closed string geometries are described by new non-commutative as well as non-associative algebras, which can be characterized by certain 3-cocycles in Lie algebra cohomology. We present an associated star-product algebra on functions in phase space. We also discuss some aspects of uncertainty relations, as well as the question, if the non-associative structures are visible in conformal field theory and in double field theory.