Quantum Field Theory is currently the best, extremely successful framework to describe all fundamental interactions, apart maybe from Gravity. Gravity becomes strong at the scale of the whole Universe or in the violent events like collisions of binary black holes, which can be observed by detecting the emitted Gravitation Waves. Even though these processes are classical, tools to calculate the shape and the amplitude of the signal are rooted in Quantum Field Theory as well.

What happens when the gravitational field is so strong that quantum effects cannot be neglected is largely unknown. Perhaps String Theory can give us a clue, or maybe the best bet is to quantize gravity in the non-relativistic regime more compatible with our everyday experience.

Quite remarkably, strong gravitational fields are capable to describe non-gravitational physics by means of the Holographic Duality. Holography has numerous applications ranging from hadrons and their interactions to strongly-correlated electrons. It also underlies those few models of Quantum Field Theory where analytical control over quantum fluctuations can be extended to a fully non-perturbative regime without any small parameters.

The mathematical structure of Quantum Field Theory is extremely rich, and over time has given rise to the whole areas of modern geometry, algebra, and representation theory, while new mathematical ideas constantly enrich our knowledge about the basic constituents of matter.