The main goal of the school will be to better prepare the interested graduate students for the upcoming program on the mathematics of string theory to be held at the Institut Henri Poincaré April 17 - July 15.

The program at IHP has already been approved, and will culminate in the important annual StringMath conference. The organisers, as well as the direction of IHP, feel strongly that the participation of young researchers will contribute essentially to the success of the program. Given the diversity of the topics and the multi-disciplinary nature of many of the developments that will be covered, it will be extremely useful to have an opportunity to give a series of pedagogical review lectures at the start of the IHP program. Coupling the proposed mini-school to the IHP thematic trimester and the StringMath conference will contribute to enhancing its international visibility.

Progress in string theory is inexorably tied to its continued interaction with a wide range of areas in mathematics. In turn, string theory has proven a reliable generator of innovative mathematical ideas, and continually inspires new avenues of mathematical research. Increasingly often, new mathematical ideas and results find their first application in string theory.

Conformal field theory, vertex algebras, mirror symmetry, generalized complex geometry, topological field theory, noncommutative geometry are just some of the areas of such fruitful interaction.

Recent exciting developments include open string mirror symmetry, wall crossing formulae, topological classication of D-branes and the derived category approach to D-branes on Calabi-Yau manifolds, geometric transitions, the relation of N=2 instanton partition functions to conformal field theory, the matrix model approach to gauge theory, the relation between Langlands program and supersymmetric gauge theories, BPS counts and mock modular forms.

The primary goal of the proposed mini-school and the subsequent trimester at IHP will be to bring together experts from around the world, mathematicians and physicists alike, to study some of these new developments, to deepen our understanding of the physical and mathematical structures at play, and to explore the interconnections between these ideas. The main focus of the program will be on recent developments in string theory which are of strong mathematical interest.