Algebra+Homotopy=OperadThis survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher homotopies. We try to show how universal this theory is by giving many applications in Algebra, Geometry, Topology, and Mathematical Physics. (This text is access
On Non-Abelian Symplectic Cutting
Chern-Weil Maslov index and its orbifold analogue
Givental graphs and inversion symmetry
Reduction of symplectic principal $\mathbb{R}$-bundles
A spectral sequence for Lagrangian Floer homology
The space of Anosov diffeomorphisms
Open Gromov-Witten invariants in dimension six
Pseudodifferential operators on manifolds with fibred corners
On the Index Formula for an Isometric Diffeomorphism
An index formula for perturbed Dirac operators on Lie manifolds
Lower bounds for Gromov width in the SO(n) coadjoint orbits
Symplectic integrators in the realm of Hofer's geometry
Submanifolds and the Hofer norm
Sub-Riemannian geometry on infinite-dimensional manifolds
Proofs On Arnold Conjectures
Yang-Mills heat flow on gauged holomorphic maps
The Conley-Zehnder indices of the rotating Kepler problem
Algebra, Topology and Algebraic Topology of 3D Ideal Fluids
The Gromov width of 4-dimensional tori
