Constructions in symplectic and contact topology via h-principles

Certain `flexible' structures in symplectic and contact topology satisfy h-principles, meaning that their geometry reduces to underlying topological data. Although these flexible structures have no interesting geometry by themselves, I will show how h-principles provide a unified approach to various constructions in symplectic and contact topology and can be used to build new exotic structures that are geometrically interesting. More precisely, I will explain how to use h-principles to construct contact manifolds with many Weinstein fillings in high dimensions, prove that all contact manifolds have symplectic caps, and construct exotic cotangent bundles containing many closed exact Lagrangians.