AbstractVarieties, if they are at all complicated, are expected to have very few rational points. This might mean “there are only finitely many rational points” or “the rational points are contained in a proper closed subvariety.” Statements like these are extremely difficult to prove in any degree of generality, with Faltings’ finiteness theorem for rational points on high-genus curves a ...
AbstractWe briefly review the origin in physics of attractor points on the moduli space of Calabi-Yau threefolds. We turn to their mathematical interpretation as special cases of Hodge loci. This leads to fascinating conjectures on the modularity of the Calabi-Yau threefolds at these points in terms of their periods and L-functions. For hypergeometric one-parameter families of Calabi-Yau threef...