New challenges in Unified theories

Abstract:
First I plan to present a short overview on various possibilities to reduce the independent parameters in Unified theories. These include higher dimensional theories where the extra dimensions are continuous but also fuzzy coset spaces. Then emphasis will be given on the Finite Unified Theories. Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories, which can be made all-loop finite, both in the dimensionless (gauge and Yukawa couplings) and dimensionful (soft supersymmetry breaking terms) sectors. This remarkable property, based on the reduction of couplings at the quantum level, provides a drastic reduction in the number of free parameters, which in turn leads to an accurate prediction of the top quark mass in the dimensionless sector, and predictions for the Higgs boson mass and the supersymmetric spectrum in the dimensionful sector.