In the past decade, due to the development of Gromov-Witten theory, mirror symmetry, and related tools, the world of enumerative geometry had been completely transformed. Many old problems have been solved and new ones have emerged.
In the beginning, only enumerative problems over the complex field were studied and the environment was essentially algebraic or symplectic. Important new developments are related to a recent appearance of tropical geometry and to a breakthrough in some enumerative problems over the reals. Another source of recent ideas is string/guage dualities which point to new directions in enumerative geometry.
All the fields mentioned above are developing very quickly, and one of the purposes is to bring together the people working in these different, but certainly closely related, directions expecting that it will be helpful for the further progress. To make familiar the important developments in these various directions, in addition to advanced talks, there will be five series of introductory lectures by Carel Faber, Andreas Gathmann, Rahul Padharipande, Ravi Vakil, and Jean-Yves Welschinger.