Perspectives in Analysis Geometry and Topology : On the Occasion of the 60th Birthday of Oleg Viro A Marcus Wallenberg Symposium on Perspectives in Analysis Geometry and Topology was held at Stockholm University in May 2008. The choice of subjects of the Symposium and present volume was motivated by the work and mathematical interests of Oleg Viro to whom the Symposium and this volume are dedicated. As a professor of Uppsala University Viro has made invaluable contributions to Swedish research by complementing the countrys longstanding tradition in analysis with his own renowned expertise in geometry and topology. Consolidating in a single volume a major portion of the recent impressive encounters among the fields of analysis geometry and topology would be too ambitious. The collection of papers in this work still should give some sense of the development of the fields and their interactions. The topics presented by leading experts in their respective fields include: algebraic geometry in particular real algebraic geometry differential geometry symplectic and contact geometry complex analysis three and four dimensional manifolds and invariants of links. Also included in the book is the opening speech of the Symposium by Lennart Carleson on the Unity of Mathematics. Contributors: S. Akbulut K. Baker R. Berman A. Degtyarev J. P. Demailly T. Ekholm Y. Eliashberg M. Entov J. Etnyre D. Gay G. Henkin I. Itenberg L. Kauffman K. Kaveh M. Khanevsky V. Kharlamov A. Khovanskii C. Manolescu N. Mishachev N. Mok S. Orevkov L. Polterovich P. Py N. Reshetikhin A. Shumakovitch E. Shustin A. Stipsicz C. Stroppel B. Webster C. Woodward. Preface 1 Selman Akbulut Exotic structures on smooth 4 manifolds 2 Kenneth Baker John Etnyre Rational linking and contact geometry 3 Robert Berman Jean Pierre Demailly Regularity of plurisubharmonic upper envelopes in big cohomology classes 4 Alex Degtarev Towards the generalized Shapiro and Shapiro conjecture. 5 Alex Degtarev Ilia Itenberg Viatcheslav Kharlamov On the number of components of a complete intersection of real quadrics 6 Tobias Ekholm Rational Symplectic Field Theory and linearized Legendrian contact homology 7 Yakov Eliashberg N. Mishachev Wrinkling IV: Mappings with prescribed singularities 8 Michael Entov Leonid Polterovich Pierre Py On continuity of quasimorphisms for symplectic maps. With an appendix by Michael Khanevsky 9 David Gay Andras Stipsicz On symplectic caps 10 Gennadi Henkin Cauchy Pompeiu type formulas for a on affine algebraic Riemann surfaces and some applications. 11 Kiumars Kaveh A. G. Khovanskii Algebraic equations and convex bodies 12 Louis Kauffman Graphical Bracket Invariants of Virtual Links 13 Ciprian Manolescu Christopher Woodward Floer homology on the extended moduli space 14 Ngaiming Mok Projective algebraicity of minimal compactifications of complex hyperbolic space forms of finite volume 15 Stepan Orevkov Some examples of real algebraic and real pseudoholomorphic curves 16 Nicolai Reshetikhin Topological invariants related to quantum groups at roots of unity 17 Alexander Shumakovitch: Khovanov Homology Theories and Their Applications 18 Eugenii Shustin Patchworking theorem for tropical curves with multiple points.