Geometry of moduli spaces and the volumes of Calabi-Yau manifolds. On a new way to compute them

$N=1$-supersymmetry of space-time in Quantum field theory, which arises when 6 of 10 dimensions of a String Theory are compactified yielding a Calabi-Yau manifold, is generally regarded as a natural way to solve some of the pending phenomenological problems in Particle Physics, such as the problem of hierarchies and the number of generations of fundamental particles. Dynamics of supermultiplets and their Lagrangians are determined by the special geometry on the moduli spaces of Calabi-Yau manifolds. I shall describe a new way to compute the Kaehler geometry on the moduli spaces; its efficiency will be demonstrated on an example of a 101-dimensional moduli space of Quintics.