Analysis Meets Geometry

This book is dedicated to the memory of Mikael Passare, an outstanding Swedish mathematician who devoted his life to developing the theory of analytic functions in several complex variables and exploring geometric ideas first-hand. It includes several papers describing Mikael's life as well as his contributions to mathematics, written by friends of Mikael's who share his attitude and passion for science. A major section of the book presents original research articles that further develop Mikael's ideas and which were written by his former students and co-authors. All these mathematicians work at the interface of analysis and geometry, and Mikael's impact on their research cannot be underestimated. Most of the contributors were invited speakers at the conference organized at Stockholm University in his honor. This book is an attempt to express our gratitude towards this great mathematician, who left us full of energy and new creative mathematical ideas.

Introduces the reader to the theory of functions of several complex variables Explains geometric ideas Presents papers on the border between analysis and geometry

Inhalt
Part I.- Mikael Passare: Curriculum Vitae.- Mikael Passare's Publications.- List of Visited Countries.- G. Passare - My Life with Mikael.- C.O. Kiselman - Mikael Passare (19592011).- M. Carlehed - Mikael Passare.- Part II.- Amoebas and Coamoebas of Linear Spaces.- One Parameter Regularizations of Products of Residue Currents.- On the Effective Membership Problem for Polynomial Ideals.- On the Optimal Regularity of Weak Geodesics in the Space of Metrics on a Polarized Manifold.- A Comparison Principle for Bergman Kernels.- Suita Conjecture from the One-dimensional Viewpoint.- Siciak's Theorem on Separate Analyticity.- Mikael Passare, a Jaunt in Approximation Theory.- Amoebas and their Tropicalizations a Survey.- Coamoebas of Polynomials Supported on Circuits.- Limit of Green Functions and Ideals, the Case of Four Poles.- Geodesics on Ellipsoids.- Welschinger Invariants Revisited.- Some Results on Amoebas and Coamoebas of Affine Spaces.- Convexity of Marginal Functions in the Discrete Case.- Modules of Square Integrable Holomorphic Germs.- An Effective Uniform ArtinRees Lemma.- Amoebas of Half-dimensional Varieties.- A log Canonical Threshold Test.- Root-counting Measures of Jacobi Polynomials and Topological Types and Critical Geodesics of Related Quadratic Differentials.- Interior Eigenvalue Density of Jordan Matrices with Random Perturbations.