In recent years, researchers have discovered an unexpected mathematical connection between two different areas of physics. One community of researchers, working to make more precise predictions for particle physics experiments like the Large Hadron Collider, has discovered that their calculations involve increasingly complicated mathematical structures, described by the mathematical discipline of algebraic geometry. Some of these calculations, involving a mathematical object called an elliptic curve, have been the focus of much recent progress. However, more complicated calculations involve yet more complicated geometries. Some of these involve more than one elliptic curve, while others involve a type of geometry studied in a very different area of physics: Calabi-Yau manifolds, previously studied as a potential shape for the extra dimensions of string theory. This workshop will bring together experts in this intersection of topics: particle physicists who aim to tackle calculations with multiple elliptic curves and Calabi-Yau manifolds, string theorists, and mathematicians who study topics that tie the two areas together such as algebraic geometry and combinatorics. The workshop will foster dialogue between these groups, a fresh exchange of ideas that should yield new insights and new progress.