"Brane Inflation and Moduli Stabilization on Twisted Tori":
In string theory, it is notoriously difficult to obtain cosmological solutions with positive energy density. On the other hand, the conceptually simplest models of inflation necessitate going to super-Planckian field values, and therefore can only be well-described by a UV complete theory of gravity (such as string theory). We will discuss string theory compactifications on twisted tori, which have given us some hope of obtaining solutions with positive energy density. We will present a no-go theorem that rules out de Sitter solutions in a large class of such models in type IIA supergravity. We will also discuss the role of discrete Wilson lines -- which are Wilson lines placed on torsion cycles -- in the stabilization of moduli on such compactifications