Appears in collection : Korea-France Joint Workshop on String Theory

Effective theories that admit a UV completion into quantum gravity are subject to a set of universal consistency constraints. Those constraints can sometimes lead to explicit, uniform bounds on concrete physical quantities of the effective theories. In the context of supersymmetric string compactifications, such physical bounds in turn translate into bounds on corresponding geometric quantities of Calabi-Yau varieties, and conversely. In this talk, focusing for concreteness on six-dimensional F-theory vacua, or equivalently on elliptically fibered Calabi-Yau three-folds, we will illustrate the bounding program with examples of explicit bounds.