Perspectives in Analysis, Geometry, and Topology: On the Occasion of the 60th Birthday of Oleg Viro (Progress in Mathematics Book 296)

The contributions in this volume—dedicated to the work and mathematical interests of Oleg Viro on the occasion of his 60th birthday—are 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. A Marcus Wallenberg Symposium On Perspective In Analysis, Geometry, And Topology Was Held At Stockholm, Sweden 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 Is 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. The Topics Presented By Leading Experts In Their Respective Fields Includes: Algebraic Geometry,in Particular, Real Algebraic Geometry, Differential Geometry, Symplectic And Contact Geometry, Complex Analysis, Three- And Four-dimensional Manifolds, And Invariants Of Links. Preface -- A Glimpse Into Viro's Work -- On The Content Of This Volume -- Program Of The Symposium -- On The Unity Of Mathematics -- Exotic Structures On Smooth Four-manifolds / Selman Akbulut -- Rational Linking And Contact Geometry / Kenneth Baker And John Etnyre -- Regularity Of Plurisubharmonic Upper Envelopes In Big Cohomology Classes / Robert Berman And Jean-pierre Demailly -- Toward A Generalized Shapiro And Shapiro Conjecture / Alex Degtyarev -- On The Number Of Components Of A Complete Intersection Of Real Quadrics / Alex Degtyarev, Ilia Itenberg, And Viatcheslav Kharlamov -- Rational Sft, Linearized Legendrian Contact Homology, And Lagrangian Floer Cohomology / Tobias Ekholm -- Topology Of Spaces Of S-immersions / Yakov Eliashberg And Nikolai Mishachev -- On Continuity Of Quasimorphisms For Symplectric Maps / Michael Entov, Leonid Polterovich, Pierre Py, With An Appendix By Michael Khanevsky -- On Symplectic Caps / David T. Gay And András I. Stipsicz -- Cauchy-pompeiu-type Formulas For [partial Derivative] On Affine Algebraic Riemann Surfaces And Some Applications / Gennadi M. Henkin -- Remarks On Khovanov Homology And The Potts Model / Louis H. Kauffman -- Algebraic Equations And Convex Bodies / Kiumars Kaveh And Askold Khovanskii -- Algebraic Equations And Convex Bodies / Kiumars Kaveh And Askold Khovanskii -- Floer Homology On The Extended Moduli Space / Ciprian Manolescu And Christopher Woodward -- Projective Algebraicity Of Minimal Compactifications Of Complex-hyperbolic Space Forms Of Finite Volume / Ngaiming Mok -- Some Examples Of Real Algebraic And Real Pseudoholomorphic Curves / Stepan Yu. Orevkov -- Schur-weyl-type Duality For Quantized Gl(1[l]1), The Burau Representation Of Braid Groups, And Invariants Of Tangled Graphs / Nicolai Reshetikhin, Catharina Stroppel, And Ben Webster -- Khovanov Homology Theories And Their Applications / Alexander Shumakovitch -- Tropical And Algebraic Curves With Multiple Points / Eugenii Shustin. Ilia Itenberg, Burglind Jöricke, Mikael Passare, Editors. Papers From The Marcus Wallenberg Symposium On Perspectives In Analysis, Geometry, And Topology, Held At Stockholm University In May 2008. Includes Bibliographical References. 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 Front Matter....Pages i-xxxi Exotic Structures on Smooth Four-Manifolds....Pages 1-17 Rational Linking and Contact Geometry....Pages 19-37 Regularity of Plurisubharmonic Upper Envelopes in Big Cohomology Classes....Pages 39-66 Toward a Generalized Shapiro and Shapiro Conjecture....Pages 67-79 On the Number of Components of a Complete Intersection of Real Quadrics....Pages 81-107 Rational SFT, Linearized Legendrian Contact Homology, and Lagrangian Floer Cohomology....Pages 109-145 Topology of Spaces of S-Immersions....Pages 147-167 On Continuity of Quasimorphisms for Symplectic Maps....Pages 169-197 On Symplectic Caps....Pages 199-212 Cauchy–Pompeiu-Type Formulas for $$\bar{\partial }$$ on Affine Algebraic Riemann Surfaces and Some Applications....Pages 213-236 Remarks on Khovanov Homology and the Potts Model....Pages 237-262 Algebraic Equations and Convex Bodies....Pages 263-282 Floer Homology on the Extended Moduli Space....Pages 283-329 Projective Algebraicity of Minimal Compactifications of Complex-Hyperbolic Space Forms of Finite Volume....Pages 331-354 Some Examples of Real Algebraic and Real Pseudoholomorphic Curves....Pages 355-387 Schur–Weyl-Type Duality for Quantized gl (1|1), the Burau Representation of Braid Groups, and Invariants of Tangled Graphs....Pages 389-401 Khovanov Homology Theories and Their Applications....Pages 403-430 Tropical and Algebraic Curves with Multiple Points....Pages 431-464 A Marcus Wallenberg Symposium on Perspective in Analysis, Geometry, and Topology was held at Stockholm, Sweden 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 is 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. The topics presented by leading experts in their respective fields includes: algebraic geometry, in particular, real algebraic geometry, differential geometry, symplectic and contact geometry, complex analysis, three- and four-dimensional manifolds, and invariants of links 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.