Mirror Symmetry, Calabi-Yau Threefolds, and Connections to Physics

Mathematics is crucial in developing the models employed in physics, and observations from physics can catalyze new branches of mathematics. Mirror symmetry is a classic example of this two-way interaction. In the context of K3 surfaces, mirror symmetry is a relation between families whose Picard lattices are complementary in the even unimodular lattice of signature (2,18). Not every family of K3 surfaces has a mirror, but this construction has been very useful in studying K3 surfaces that are toric hypersurfaces, for example. Physicists have studied K3 surfaces, elliptic fibrations, and mirror symmetry on them in connection with string theory; this provides a concrete setting that can lead to the discovery of new properties of Calabi-Yau threefolds. The study of K3 surfaces in families naturally leads to Calabi-Yau threefolds and manifolds of higher dimension. In recent years, several connections have been established between these varieties, Feynman integrals, and Φ4 theory.

The aim of this workshop is to bring together experts from different areas of mathematics and physics in order to foster a fruitful exchange of knowledge and achieve new insights.