Papers based on selected lectures given at the Current Development Mathematics Conference, held in November 2009 at Harvard University.

Originating with Andreas Floer in the 1980s, Floer homology has proved to be an effective tool in tackling many important problems in three- and four-dimensional geometry and topology. This book provides a comprehensive treatment of Floer homology, based on the Seiberg Witten monopole equations. After first providing an overview of the results, the authors develop the analytic properties of the Seiberg Witten equations, assuming only a basic grounding in differential geometry and analysis. The Floer groups of a general three-manifold are then defined and their properties studied in detail. Two final chapters are devoted to the calculation of Floer groups and to applications of the theory in topology. Suitable for beginning graduate students and researchers, this book provides the first full discussion of a central part of the study of the topology of manifolds since the mid 1990s.

Originating with Andreas Floer in the 1980s, Floer homology has proved to be an effective tool in tackling many important problems in three- and four-dimensional geometry, and topology. This book provides a comprehensive treatment of Floer homology, based on the Seiberg-Witten monopole equations. After first providing an overview of the results, the authors develop the analytic properties of the Seiberg-Witten equations, assuming only a basic grounding in differential geometry and analysis. The Floer groups of a general three-manifold are then defined, and their properties studied in detail. Two final chapters are devoted to the calculation of Floer groups, and to applications of the theory in topology. Suitable for beginning graduate students and researchers, this book provides the first full discussion of a central part of the study of the topology of manifolds since the mid 1990s.

These are the proceedings of the joint seminar by M.I.T. and Harvard on the current developments in mathematics for the year 2002. The organizing committee for the seminar consisted of distinguished mathematicians from the mathematics departments of both institutions: B. Mazur, W. Schmid, and S.T. Yau from Harvard, and D. Jerison, T. Mrowka, and R. Stanley from M.I.T. This year, the seminar was dedicated to Prof. Wilfried Schmid and Prof. George Lusztig. The 2002 speakers included Albert Bressan, Mark Haiman, Richard Hain, Stephen Kudla, Yair Minsky, John Morgan, Leslie Saper, Kari Vilonen, and David Vogan.