Physically-inspired Structures in Complex, Symplectic, and Contact Geometry

There is a long history relating geometry and physics. While physics fundamentally relies on geometric tools in topics such as: classical mechanics, thermodynamics, and optics. The influence is often reciprocal, with many rich mathematical structures being directly inspired by physical phenomena. In this project, we exhibit a few instances of this exchange, focusing on developments in complex, symplectic, and contact geometry.