Mikael Passare – författare

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 set in complex Euclidean space is called C-convex if all its intersections with complex lines are contractible, and it is said to be linearly convex if its complement is a union of complex hyperplanes. These notions are intermediates between ordinary geometric convexity and pseudoconvexity. Their importance was first manifested in the pioneering work of André Martineau from about forty years ago. Since then a large number of new related results have been obtained by many different mathematicians. The present book puts the modern theory of complex linear convexity on a solid footing, and gives a thorough and up-to-date survey of its current status. Applications include the Fantappié transformation of analytic functionals, integral representation formulas, polynomial interpolation, and solutions to linear partial differential equations.