Shaping Physics from Geometry: Moduli and Their Role in String Theory

Abstract: A robust prediction of string theory is the existence of extra dimensions. Their shape and size is governed by parameters called moduli. The value of these moduli enter all physical observables, such as the Yukawa couplings, the type and relic abundance of dark matter, the cosmological constant, etc. To extract predictions of string theory for Particle Physics and Cosmology, we therefore need to better understand the structure of the moduli spaces, the selection mechanism which sets their values, and regions in moduli space where viable string solutions can be found. I will review the underlying theory and precent recent developments towards a better understanding of how to study the impact of moduli on Physics.