Trends in Mathematics Mats Andersson Jan Boman Christer Kiselman Pavel Kurasov Ragnar Sigurdsson Editors Analysis Meets Geometry The Mikael Passare Memorial Volume Trends in Mathematics Trends in Mathematics is a series devoted to the publication of volumes arising from conferences and lecture series focusing on a particular topic from any area of mathematics. Its aim is to make current developments available to the community as rapidly as possible without compromise to quality and to archive these for reference. Proposals for volumes can be submitted using the Online Book Project Submission Form at our website www.birkhauser-science.com. Material submitted for publication must be screened and prepared as follows: All contributions should undergo a reviewing process similar to that carried out by journals and be checked for correct use of language which, as a rule, is English. Articles without proofs, or which do not contain any significantly new results, should be rejected. High quality survey papers, however, are welcome. We expect the organizers to deliver manuscripts in a form that is essentially ready for direct reproduction. Any version of TEX is acceptable, but the entire collection of files must be in one particular dialect of TEX and unified according to simple instructions available from Birkhäuser. Furthermore, in order to guarantee the timely appearance of the proceedings it is essential that the final version of the entire material be submitted no later than one year after the conference. Moreinformationaboutthisseriesathttp://www.springer.com/series/4961 Mats Andersson • Jan Boman • Christer Kiselman Pavel Kurasov • Ragnar Sigurdsson Editors Analysis Meets Geometry The Mikael Passare Memorial Volume Editors Mats Andersson Jan Boman Department of Mathematics Department of Mathematics Chalmers University of Technology Stockholm University Göteborg, Sweden Stockholm, Sweden Christer Kiselman Pavel Kurasov Department of Information Technology Department of Mathematics Uppsala University Stockholm University Uppsala, Sweden Stockholm, Sweden Ragnar Sigurdsson Science Institute University of Iceland Reykjavik, Iceland ISSN 2297-0215 ISSN 2297-024X (electronic) Trends in Mathematics ISBN 978-3-319-52469-6 ISBN 978-3-319-52471-9 (eBook) DOI 10.1007/978-3-319-52471-9 Library of Congress Control Number: 2017951453 Mathematics Subject Classification (2010): 01-00, 32-XX, 51-XX, 35-XX © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This book is published under the trade name Birkhäuser, www.birkhauser-science.com The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Contents Preface .................................................................. vii Part I: Memorial Contributions Mikael Passare:Curriculum Vitae ........................................ 3 Mikael Passare’sPublications ............................................ 5 List of Visited Countries ................................................. 11 G. Passare My Life with Mikael ................................................ 15 C.O. Kiselman Mikael Passare (1959–2011) ......................................... 35 M. Carlehed Mikael Passare ...................................................... 59 Part II: Research Articles M. Nisse and M. Passare Amoebas and Coamoebas of Linear Spaces .......................... 63 M. Andersson, H. Samuelsson Kalm, E. Wulcan, and A. Yger One Parameter Regularizations of Products of Residue Currents .... 81 M. Andersson and E. Wulcan On the Effective Membership Problem for Polynomial Ideals ........ 91 R.J. Berman On the Optimal Regularity of Weak Geodesics in the Space of Metrics on a PolarizedManifold .................................... 111 B. Berndtsson A Comparison Principle for Bergman Kernels ....................... 121 Z. B(cid:2)locki Suita Conjecture from the One-dimensional Viewpoint .............. 127 J. Boman Siciak’s Theorem on Separate Analyticity ........................... 135 vi Contents J.-P. Calvi Mikael Passare, a Jaunt in Approximation Theory .................. 147 T. de Wolff Amoebas and their Tropicalizations – a Survey ...................... 157 J. Forsg˚ard Coamoebas of Polynomials Supported on Circuits ................... 191 D. Quang Hai and P.J. Thomas Limit of Green Functions and Ideals, the Case of Four Poles ......... 213 J. Hoppe Geodesics on Ellipsoids ............................................. 229 I. Itenberg, V. Kharlamov, and E. Shustin Welschinger Invariants Revisited .................................... 239 P. Johansson Some Results on Amoebas and Coamoebas of Affine Spaces ......... 261 C.O. Kiselman and S. Samieinia Convexity of Marginal Functions in the Discrete Case ............... 287 L. Lempert Modules of Square Integrable Holomorphic Germs ................... 311 J. Lundqvist An Effective Uniform Artin–Rees Lemma ........................... 335 G. Mikhalkin Amoebas of Half-dimensional Varieties .............................. 349 A. Rashkovskii A log Canonical Threshold Test ..................................... 361 B. Shapiro and A. Solynin Root-counting Measures of Jacobi Polynomials and Topological Types and Critical Geodesics of Related Quadratic Differentials ..... 369 J. Sj¨ostrand and M. Vogel Interior Eigenvalue Density of Jordan Matrices with Random Perturbations ....................................................... 439 Preface Dear Reader, This volume is dedicated to the life and work of Mikael Passare, who un- expectedly passed away in September 2011 at the age of 52. It will give you a chance to study several texts that are inspired by his mathematical interests – either directly so, or in a more indirect way. One chapter is even coauthored by Mikael. We are indeed happy that so many outstanding scientists have answeredour call to contribute a chapter to the book. Before arriving to these mathematical chapters, you can get an idea about Mikael’s life and his far-reaching research, which spans from analysis in several complex variables and complex geometry to amoebas and tropical geometry. We hope that you will enjoy getting acquainted with the ideas of a great mathematician and a great human being. Mats Andersson Jan Boman Christer Kiselman Pavel Kurasov Ragnar Sigurdsson Mikael Passare 1959–2011 Part I Memorial Contributions This part collects several articles describing Mikael Passare, as a mathematician andasa greatpersonality.ItcontainsalsoMikael’s Curriculum Vitae, a listofhis publications and the list of all 152 countries that Mikael managed to visit.