The conference entitled "Summer School on Moduli Problems in Symplectic Geometry" will take place at the IHES (Institute des Hautes Etudes Scientifiques) in Bures-sur-Yvette, France from July 6-17, 2015. The conference website is located at https://indico.math.cnrs.fr/conferenceDisplay.py?confId=585. This conference will provide PhD students, postdocs, and young researchers with an overview of the most recent technology in symplectic geometry, as well as faciliate collaborations to further develop this technology. This grant will provide travel funding for young US researchers lacking other federal support, with an emphasis on members of underrepresented groups, to attend this conference. This will enable the next generation of US researchers to keep up with the latest developments and stay at the forefront of symplectic geometry.
Symplectic geometry has made enormous advances since the introduction of (pseudo)holomorphic curves by Gromov in 1985. However in order to use holomorphic curves in symplectic geometry, a substantial amount of analysis is needed to regularize the moduli spaces of holomorphic curves. In the 80's and 90's these moduli spaces were regularized using geometric perturbation techniques. However since then, symplectic geometry has moved beyond the scope of problems to which geometric perturbation techniques are applicable, leaving a serious gap in the foundations of the subject. Perhaps the most successful and promising technology for filling this gap is the polyfold theory of Hofer, Wysocki and Zehnder. The conference has two main goals. The first goal is to educate a large audience in polyfold theory, in order to enable more researchers to begin developing and using these new techniques. The second goal is to connect the abstract perturbations of polyfolds to the classical geometric perturbations in order to facilitate computations of invariants.
