211005 Frits Beukers

In a famous 1995 paper on mirror symmetry Candelas, de la Ossa, Greene and Parkes discovered a remarkable relation between certain numbers (named instanton numbers) arising from a classical family of Calabi-Yau 3-folds and counting the number of rational curves of given degree on a general quintic threefold in projective space. This discovery was driven by arguments from physics, but mathematically it was not known that these numbers are integers for a long time. In this talk I describe some work together with Masha Vlasenko that gives some insight in this integrality.