The recent detections of gravitational waves from merging black holes and neutron stars have established gravitational waves as a new cosmological messenger and opened unique opportunities for probing gravity and matter in unexplored regimes. I will discuss the basic physics of gravitational waves, the facilities and methods for detecting and interpreting the signals, and the remarkable insights we have gained from the observations to date. I will conclude with an outlook onto the exciting prospects and challenges for the next years as the field of gravitational wave physics moves from the discovery era to one of precision physics.
(joint work with Michel Cahen)
Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics. Complex geometry is on the crossroad of algebraic and differential geometry. In differential geometry it yields the notion of almost complex structures.
Kähler geometry is at the intersection of symplectic and complex geometry.
I shall recall examples and properties of those three geometries and examples of symplectic manifolds which are not Kähler.
All symplectic manifolds admit almost complex structures.
I shall exhibit geometrical structures associated to (non complex) almost complex structures on a symplectic manifold.