Ebook: Perspectives in Analysis, Geometry, and Topology: On the Occasion of the 60th Birthday of Oleg Viro

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 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

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

Content:
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 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

Content:
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
....