By Denis Auroux,Fabrizio Catanese,Marco Manetti,Paul Seidel,Bernd Siebert,Ivan Smith,Gang Tian
Modern techniques to the research of symplectic 4-manifolds and algebraic surfaces mix quite a lot of strategies and assets of concept. Gauge concept, symplectic geometry, pseudoholomorphic curves, singularity concept, moduli areas, braid teams, monodromy, as well as classical topology and algebraic geometry, mix to make this essentially the most vivid and lively components of study in arithmetic. it really is our desire that the 5 lectures of the current quantity given on the C.I.M.E. summer time university held in Cetraro, Italy, September 2-10, 2003 may be important to humans operating in comparable parts of arithmetic and should develop into typical references on those topics.
The quantity is a coherent exposition of an energetic box of present learn concentrating on the advent of latest tools for the research of moduli areas of complicated buildings on algebraic surfaces, and for the research of symplectic topology in measurement four and higher.