The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.

The contributions in this volumededicated to the work and mathematical interests of Oleg Viro on the occasion of his 60th birthdayare invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap among analysis, geometry, and topology. The encounters among these three fields are widespread and often provide impetus for major breakthroughs in applications.

Topics covered include new developments in low-dimensional topology related to invariants of links and three- and four-dimensional manifolds and the recent advances made in algebraic, complex, symplectic, and tropical geometry.

This collection is intended for graduate students and researchers in analysis, geometry, and topology, especially those whose area of study applies to two or more of these fields.

Focuses on recent developments and trends that bridge analysis, topology, and geometry Chronicles a groundbreaking symposium Highlights possible new research directions Invited articles written by distinguished researchers Of interest to graduate students and researchers Includes supplementary material: sn.pub/extras

Klappentext

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 country's 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

Inhalt
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.