Gravitational descendants in symplectic field theory

It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold is the prequantization space of a symplectic manifold. In this paper we generalize the definition of gravitational descendants in SFT from circle bundles in the Morse-Bott case to general contact manifolds. After we have shown that for the basic examples of holomorphic curves in SFT, that is, branched covers of cylinders over closed Reeb orbits, the gravitational descendants have a geometric interpretation in terms of branching conditions, we compute the corresponding sequences of Poisson-commuting functions when the contact manifold is the unit cotangent bundle of a Riemannian manifold.Comment: 44 pages, no figure

Higher algebraic structures in Hamiltonian Floer theory I

This is the first of two papers devoted to showing how the rich algebraic formalism of Eliashberg-Givental-Hofer's symplectic field theory (SFT) can be used to define higher algebraic structures on the symplectic cohomology of open symplectic manifolds. Using the SFT of Hamiltonian mapping tori we show how to define a homotopy extension of the well-known Lie bracket on symplectic cohomology. Apart from discussing applications to the existence of closed Reeb orbits, we outline how the $L_{\infty}$-structure is conjecturally related via mirror symmetry to the extended deformation theory of complex structures.Comment: Results of arXiv:1310.6014 got merged into arXiv:1412.2682, now entitled "Higher algebraic structures in Hamiltonian Floer theory" and published in Advances in Geometry (DOI: 10.1515/advgeom-2019-0017). Extensions of other announced results have been turned into an ongoing PhD thesis projec

Local symplectic field theory

Generalizing local Gromov-Witten theory, in this paper we define a local version of symplectic field theory. When the symplectic manifold with cylindrical ends is four-dimensional and the underlying simple curve is regular by automatic transversality, we establish a transversality result for all its multiple covers and discuss the resulting algebraic structures

Dual Q-switched laser outputs from a single lasing medium using an intracavity MEMS micromirror array

An intracavity array of individually controlled microelectromechanical system scanning micromirrors was used to actively Q-switch a single side-pumped Nd:YAG gain medium. Two equal power independent laser outputs were simultaneously obtained by separate actuation of two adjacent micromirrors with a combined average output power of 125 mW. Pulse durations of 28 ns FWHM at 8.7 kHz repetition frequency and 34 ns FWHM at 7.9 kHz repetition frequency were observed for the two output beams with beam quality factors M2 of 1.2 and 1.1 and peak powers of 253 W and 232 W, respectively