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.

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.