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Analysis meets geometry : the Mikael Passare memorial volume

Author: Mats Andersson; Mikael Passare
Publisher: Cham, Switzerland : Birkhäuser, [2017] ©2017
Series: Trends in mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: (OCoLC)966595573
Named Person: Mikael Passare
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Mats Andersson; Mikael Passare
ISBN: 9783319524719 3319524712
OCLC Number: 1006306050
Description: 1 online resource.
Contents: 1. Introduction2. Residue currents; 2.1. Currents on a singular variety; 2.2. Pseudomeromorphic currents; 2.3. Residue currents associated with Hermitian complexes; 2.4. BEF-varieties on singular varieties; 2.5. The structure form [omega] on a singular variety; 3. Gap sheaves and primary decomposition of sheaves; 4. Resolutions of homogeneous ideals; 5. Division problems on singular varieties; 5.1. Distinguished varieties; 6. Proofs; References; On the Optimal Regularity of Weak Geodesics in the Space of Metrics on a Polarized Manifold; 1. Introduction Preface; Part I Memorial Contributions; Mikael Passare; Curriculum Vitae; Mikael Passare's Publications; List of Visited Countries; My Life with Mikael; World; Languages; Challenges; Home; Music; Projects; Personality; Thanks; Mikael Passare (1959-2011); Mikael's nine PhD students; Mikael's mathematics; Residue theory; Residues in one complex variable.; Residues in several variables.; Lineal convexity; Amoebas and tropical geometry; The Pluricomplex Seminar; Lectures held by Mikael Passare.; The Nordan Meetings; Africa; Sonja Kovalevsky; Languages; An extraordinary curiosity; Music A "Swedish Classic"A passionate traveler; Finally; Two proposals; References; Sources; Mikael Passare; Part II Research Articles; Amoebas and Coamoebas of Linear Spaces; 1. Introduction; 2. Preliminaries; 3. (Co)amoebas of complex algebraic varieties; 4. (Co)Amoebas of linear spaces; 4.1. (Co)Amoebas of lines in (C*) 1+m; 5. Volume of (co)amoebas of k-dimensional very affine linear spaces in (C*)2k; References; One Parameter Regularizations of Products of Residue Currents; 1. Introduction; 2. Proof of Theorems 1.2 and 1.3; References; On the Effective Membership Problem for Polynomial Ideals 2. C1,1-regularity of solutions to complex Monge-Ampère equations over products2.1. Notation: quasi-psh functions vs metrics on line bundles; 2.2. The C1,1-regularity of weak geodesics; 2.3. Further remarks; Acknowledgment; References; A Comparison Principle for Bergman Kernels; 1. Introduction; 2. The abstract setting; 3. The proof of Theorem 1.1; References; Suita Conjecture from the One-dimensional Viewpoint; Introduction; 1. Proof of the Suita conjecture; 2. A Formula for the Bergman kernel; References; Siciak's Theorem on Separate Analyticity; 1. Introduction 2. Separate analyticity with boundedness assumption3. The general case; References; Mikael Passare, a Jaunt in Approximation Theory; 2. Back to Hermite; 3. From Hermite to Kergin; 4. Complex Kergin interpolation; 5. Kergin and Fantappiè; 6. Mean value interpolation; References; Amoebas and their Tropicalizations --
a Survey; 1. Introduction; 2. Preliminaries; 2.1. Amoebas; 2.2. The tropical semi-ring; 3. Valuations and the non-Archimedean amoeba; 4. Maslov dequantization; 5. The Archimedean tropical hypersurface and the complement induced tropical hypersurface; 6. The spine
Series Title: Trends in mathematics.
Responsibility: Mats Andersson [and 4 others], editors.

Abstract:

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.

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