Moduli Stabilization and Inflation in Type IIB/F-theory

In the first part of this talk, a short overview of the ongoing debate on the existence of de Sitter vacua in string theory is presented. In the second part, the moduli stabilisation and inflation are discussed in the context of type IIB/F-theory. Considering a configuration of three intersecting $D7$ branes with fluxes, it is shown that higher loop effects inducing logarithmic corrections to the K\"ahler potential can stabilise the K\"ahler moduli in a de Sitter Vacuum. When a new Fayet-Iliopoulos term is included, it is also possible to generate the required number of e-foldings and satisfy the conditions for slow-roll inflation.