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Bart, Hempfling, Kaashoek. (Eds.) Israel Gohberg and Friends.. on The
Israel Gohberg and Friends On the Occasion of his 80th Birthday Harm Bart Thomas Hempfling Marinus A. Kaashoek Editors Birkhäuser Basel · Boston · Berlin Editors: Harm Bart Marinus A. Kaashoek Econometrisch Instituut Department of Mathematics, FEW Erasmus Universiteit Rotterdam Vrije Universiteit Postbus 1738 De Boelelaan 1081A 3000 DR Rotterdam 1081 HV Amsterdam The Netherlands The Netherlands e-mail: [email protected] e-mail: [email protected] Thomas Hempfling Editorial Department Mathematics Birkhäuser Publishing Ltd. P.O. Box 133 4010 Basel Switzerland e-mail: thomas.hempfl[email protected] Library of Congress Control Number: 2008927170 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at <http://dnb.ddb.de>. ISBN 978-3-7643-8733-4 Birkhäuser Verlag, Basel – Boston – Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2008 Birkhäuser Verlag AG Basel · Boston · Berlin P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced of chlorine-free pulp. TCF ∞ Printed in Germany ISBN 978-3-7643-8733-4 e-ISBN 978-3-7643-8734-1 9 8 7 6 5 4 3 2 1 www.birkhauser.ch Contents Preface.......................................................................ix CongratulationsfromthePublisher...........................................xii PartI.MathematicalandPhilosophical-MathematicalTales...................1 I. -
Contemporary Mathematics 442
CONTEMPORARY MATHEMATICS 442 Lie Algebras, Vertex Operator Algebras and Their Applications International Conference in Honor of James Lepowsky and Robert Wilson on Their Sixtieth Birthdays May 17-21, 2005 North Carolina State University Raleigh, North Carolina Yi-Zhi Huang Kailash C. Misra Editors http://dx.doi.org/10.1090/conm/442 Lie Algebras, Vertex Operator Algebras and Their Applications In honor of James Lepowsky and Robert Wilson on their sixtieth birthdays CoNTEMPORARY MATHEMATICS 442 Lie Algebras, Vertex Operator Algebras and Their Applications International Conference in Honor of James Lepowsky and Robert Wilson on Their Sixtieth Birthdays May 17-21, 2005 North Carolina State University Raleigh, North Carolina Yi-Zhi Huang Kailash C. Misra Editors American Mathematical Society Providence, Rhode Island Editorial Board Dennis DeTurck, managing editor George Andrews Andreas Blass Abel Klein 2000 Mathematics Subject Classification. Primary 17810, 17837, 17850, 17865, 17867, 17868, 17869, 81T40, 82823. Photograph of James Lepowsky and Robert Wilson is courtesy of Yi-Zhi Huang. Library of Congress Cataloging-in-Publication Data Lie algebras, vertex operator algebras and their applications : an international conference in honor of James Lepowsky and Robert L. Wilson on their sixtieth birthdays, May 17-21, 2005, North Carolina State University, Raleigh, North Carolina / Yi-Zhi Huang, Kailash Misra, editors. p. em. ~(Contemporary mathematics, ISSN 0271-4132: v. 442) Includes bibliographical references. ISBN-13: 978-0-8218-3986-7 (alk. paper) ISBN-10: 0-8218-3986-1 (alk. paper) 1. Lie algebras~Congresses. 2. Vertex operator algebras. 3. Representations of algebras~ Congresses. I. Leposwky, J. (James). II. Wilson, Robert L., 1946- III. Huang, Yi-Zhi, 1959- IV. -
Implications for Understanding the Role of Affect in Mathematical Thinking
Mathematicians and music: Implications for understanding the role of affect in mathematical thinking Rena E. Gelb Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy under the Executive Committee of the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2021 © 2021 Rena E. Gelb All Rights Reserved Abstract Mathematicians and music: Implications for understanding the role of affect in mathematical thinking Rena E. Gelb The study examines the role of music in the lives and work of 20th century mathematicians within the framework of understanding the contribution of affect to mathematical thinking. The current study focuses on understanding affect and mathematical identity in the contexts of the personal, familial, communal and artistic domains, with a particular focus on musical communities. The study draws on published and archival documents and uses a multiple case study approach in analyzing six mathematicians. The study applies the constant comparative method to identify common themes across cases. The study finds that the ways the subjects are involved in music is personal, familial, communal and social, connecting them to communities of other mathematicians. The results further show that the subjects connect their involvement in music with their mathematical practices through 1) characterizing the mathematician as an artist and mathematics as an art, in particular the art of music; 2) prioritizing aesthetic criteria in their practices of mathematics; and 3) comparing themselves and other mathematicians to musicians. The results show that there is a close connection between subjects’ mathematical and musical identities. I identify eight affective elements that mathematicians display in their work in mathematics, and propose an organization of these affective elements around a view of mathematics as an art, with a particular focus on the art of music. -
Fundamental Theorems in Mathematics
SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635]. -
Birkhäuser Mathematics 2009 /2010
Order Information Distribution Centers Editorial Matters To order any of our books or Europe, Asia, Africa, Birkhäuser Verlag AG journals please contact your Australia Viaduktstrasse 42 local bookseller or order at Birkhäuser Customer Service 4051 Basel/Switzerland www.birkhauser.ch c/o Springer Customer Tel: +41 / 61 / 2 05 07 07 Service Center Fax: +41 / 61 / 2 05 07 99 To subscribe or unsubscribe Haberstrasse 7 to this catalogue please 69126 Heidelberg/Germany Editors: contact Dr. Thomas Hempfling Books: [email protected] Executive Editor Tel.: +49 / 6221 / 345 43 01 Mathematics Fax: +49 / 6221 / 345 42 29 All prices are recommended [email protected] [email protected] prices, except Euro prices for Birkhäuser German titles. Journals: Dr. Barbara Hellriegel EUR prices are net prices. Tel. +49 / 6221 / 345 43 01 Editor EUR (D) prices are gross Fax +49 / 6221 / 345 42 29 Applied Mathematics/Computer Birkhäuser prices including 7% German [email protected] Science VAT. [email protected] Switzerland, Liechtenstein EUR (A) prices are gross Mathematics Balmer Bücherdienst AG Mathematics prices including 10% Dr. Karin Neidhart Customer Service Austrian VAT. Editor Kobiboden CHF prices are gross prices. History of Science 8840 Einsiedeln/Switzerland Prices are subject to change [email protected] 2009 /2010 without notice. Tel.: +41 / 848 / 840 820 Fax: +41 / 848 / 840 830 [email protected] 2009/2010 North and South America Birkhäuser Boston Birkhäuser Boston 233 Spring Street c/o Springer -
Matematiska Kollokviets Tidigare Seminarier
Matematiska kollokviet - Linköpings universitet https://liu.se/artikel/matematiska-kollokviet 0nsdag 18 december 2019, Antonio F. Costa, UNED, Madrid, Spanien Titel: Concepts in Geometry and Topology Illustrated Using Decorations of Islamic Art Sammanfattning: Islamic art, because of its abstract character, is particularly well suited to exemplify some mathematical concepts. We'll start by remembering one of the most well- known and controversial subject: the appearance in this art of all possible euclidean planar crystalline symmetry. Other recent discoveries, as the presence of quasi-crystals, and examples of relations with mathematical concepts will also be exhibited. 0nsdag 11 december 2019, Joakim Arnlind, Matematiska institutionen, Linkopings universitet Titel: Projective modules over the noncommutative cylinder Sammanfattning: I will give an introduction to the noncommutative cylinder, which is a simple example of a non-compact noncommutative manifold. Finitely generated projective modules over a noncommutative algebra correspond to vector bundles in classical geometry, and we present explicit projectors generating the so called K-theory of the noncommutative cylinder. Furthermore, as everyone might not be familiar with the basic ideas of noncommutative geometry, I will try to motivate and explain several of the concepts as they appear in this context. 0nsdag 4 december 2019, Hans Lundmark, Matematiska institutionen, Linkopings universitet Titel: Peakon solutions of the Novikov and Geng–Xue equations Sammanfattning: Peakons (short -
Bibliography
Bibliography [AA66] Vadim M. Adamjan and Damir Z. Arov, Unitary couplings of semi- unitary operators, (Russian) Mat. Issled. 1 (1966), no. 2, 3–64. [AA68] Vadim M. Adamjan and Damir Z. Arov, A general solution of a cer- tain problem in the linear prediction of stationary processes, (Rus- sian) Teor. Verojatnost. i Primenen. 13 (1968) 419–431; English translation: Theor. Probability Appl. 13 (1968), 394–407 [AAK71] Vadim M. Adamjan, Damir Z. Arov and Mark G. Krein, Analytic properties of Schmidt pairs of a Hankel operator and the generalized Schur–Takagi problem, (Russian) Mat. Sb. (N.S.) 86(128) (1971), 34– 75; English translation: Math USSR Sbornik 15 (1971), no. 1, 31–73. [AR68] Naum I. Ahiezer, and Alexander M. Rybalko, Continual analogues of polynomials orthogonal on a circle, (Russian) Ukrain.Mat.Z.20 (1968), no. 1, 3–24. [AlD84] Daniel Alpay and Harry Dym, Hilbert spaces of analytic functions, in- verse scattering and operator models, I., Integral Equations Operator Theory 7 (1984), no. 5, 589–641. [AlD85] Daniel Alpay and Harry Dym, Hilbert spaces of analytic functions, in- verse scattering and operator models, II., Integral Equations Operator Theory 8 (1985), no. 2, 145–180. [AlD93] Daniel Alpay and Harry Dym, On a new class of structured repro- ducing kernel spaces, J. Functional Analysis 111 (1993), no. 1, 1–28. [AlG95] Daniel Alpay and Israel Gohberg, Inverse spectral problem for differ- ential operators with rational scattering matrix functions, J. Differ- ential Equations 118 (1995), no. 1, 1–19. [AlG97] Daniel Alpay and Israel Gohberg, State space method for inverse spec- tral problems, in: Systems and Control in the Twenty-first Century (St. -
Conferences & Ph.D Students
CONFERENCES 2019 "Operator Theory and Krein Spaces", Vienna, Austria, December 19-22 2019 "Spectral Theory and Differential Equations" Sveti Martin na Muri, Croatia, September 8-13 2019 "AMS Spring Eastern Sectional Meeting" University of Connecticut, Hartford, CT, USA, April 13-14 2018 "Modeling, Analysis, and Approximation Theory" Humboldt University, Berlin, Germany, August 19-20 2018 "Advances in Operator Theory with Applications to Mathematical Physics" Chapman University, Orange, CA, USA, November 12-16 2017 "Stefan Banach Conference in Functional Analysis" Lviv, Ukraine, September, 18 - 23 2017 Summer School, "Modeling, Analysis, and Approximation Theory" L¨ubeck, Germany, July 31 { August 4 2015 All-Ukrainian conference "Modern problems of probability theory and mathematical analysis", Vorokhta, Ukraine, February 25-28 2015 Workshop "Spectral Theory and Weyl Function" Oberwolfach, Germany, January, 4 - 10 2014 "Operator Theory, Analysis and Mathematical Physics" Stockholm, Sweden, July 7 - 11 2013 Workshop "System and Operator Realizations of Analytic Functions" Leiden, The Netherlands, February, 17-24 2010 IWOTA, 21-th International Workshop on Operator Theory and its Applications Berlin, Germany, July 12 { 16 2009 Workshop "Boundary Relations, extension theory and applications" Leiden, The Netherlands, December 13-18 2009 Ukrainian Mathematical Congress, Kiev, Ukraine, August 27-29 2009 Haifa Matrix Theory Conference, Haifa, Israel, May 18 - 21 2008 8-th Workshop "Operator Theory in Krein Spaces and Spectral Analysis", Berlin, -
Math.CV] 25 Oct 2010 H 97Bo Frsac Rbescletdadeie Yw Haym W
Borcea’s variance conjectures on the critical points of polynomials Dmitry Khavinson, Rajesh Pereira, Mihai Putinar, Edward B. Saff and Serguei Shimorin Julius Borcea, in memoriam Abstract. Closely following recent ideas of J. Borcea, we discuss various mod- ifications and relaxations of Sendov’s conjecture about the location of critical points of a polynomial with complex coefficients. The resulting open problems are formulated in terms of matrix theory, mathematical statistics or potential theory. Quite a few links between classical works in the geometry of polynomi- als and recent advances in the location of spectra of small rank perturbations of structured matrices are established. A couple of simple examples provide natural and sometimes sharp bounds for the proposed conjectures. Mathematics Subject Classification (2000). Primary 12D10; Secondary 26C10, 30C10, 15A42, 15B05. Keywords. Sendov conjecture, Hausdorff distance, critical point, differentiator, variance, Chebyshev radius, Cauchy transform. 1. Introduction In 1958, while working as an assistant to Professor N. Obreshkov, Blagovest Sendov raised the following question. Assume that all zeros of a polynomial F with complex coefficients lie in the closed unit disk. Is it true that there exists a critical point in arXiv:1010.5167v1 [math.CV] 25 Oct 2010 every disk of radius one centered at a zero of F ? The conjecture was included in the 1967 book of research problems collected and edited by W. Hayman [32]. The This work was completed with the support of the American Institute of Mathematics, Palo Alto. D. Khavinson, M. Putinar and E. Saff also gratefully acknowledge the support by the National Science Foundation, through the grants DMS-0855597, DMS-1001071 and DMS-0808093, respec- tively. -
Birkhäuser Mathematics Catalog 2007 New and Recent Titles
Birkhäuser Mathematics Catalog 2007 New and recent titles Journals Distribution Centres Editorial Matters All countries excluding USA / Canada / Latin America Birkhäuser Verlag AG those listed below: Birkhäuser Boston, Inc. P.O. Box 133 Birkhäuser Customer Service 333 Meadowlands Parkway CH – 4010 Basel c/o SDC Secaucus, NJ 07094-2491, USA Tel: +41 / 61 / 2 05 07 07 Haberstrasse 7 Tel.: +1 / 800 / 777 4643 Fax: +41 / 61 / 2 05 07 92 D-69126 Heidelberg Fax: +1 / 201 / 348 4505 Tel.: +49 / 6221 / 345 0 e-mail: [email protected] Editors: Fax: +49 / 6221 / 345 42 29 www.birkhauser.com Dr. Thomas Hempfling e-mail: [email protected] Executive Editor Mathematics/Physics Switzerland / Liechtenstein [email protected] Balmer Bücherdienst AG Customer Service Dr. Stefan Göller Bösch 41 Editor CH-6331 Hünenberg Computational Sciences and Tel.: +41 / 41 / 726 98 00 Engineering, History of Science Fax: +41 / 41 / 726 98 01 [email protected] e-mail: [email protected] Austria / Eastern Europe Peter Nosoli / Alfred Bruckner Birkhäuser Boston, Inc. Birkhäuser Verlag AG 675, Massachussets Avenue c/o Springer Verlag Wien Cambridge, MA 02139 / USA Sachsenplatz 4-6 P.O. Box 89, A-1201 Wien Editors: Tel.: +43 / 1 / 330 24 15 /248 od. 224 Ann Kostant Fax: +43 / 1 / 330 24 26 62 Executive Editor e-mail: [email protected] Mathematics/Physics [email protected] Australia / New Zealand Order information for journals: Tom Grasso D.A. Information Services Birkhäuser Customer Service Journals Editor 648 Whitehorse Road c/o SDC Computational Sciences Mitcham Vic 3132 Haberstrasse 7 and Engineering Australia 69129 Heidelberg [email protected] Tel.: +613 / 9210 7777 Germany Fax: +613 / 9210 7788 Tel. -
Borcea's Variance Conjectures on the Critical Points of Polynomials
Borcea’s variance conjectures on the critical points of polynomials Dmitry Khavinson, Rajesh Pereira, Mihai Putinar, Edward B. Saff and Serguei Shimorin Julius Borcea, in memoriam Abstract. Closely following recent ideas of J. Borcea, we discuss various mod- ifications and relaxations of Sendov’s conjecture about the location of critical points of a polynomial with complex coefficients. The resulting open problems are formulated in terms of matrix theory, mathematical statistics or potential theory. Quite a few links between classical works in the geometry of polynomi- als and recent advances in the location of spectra of small rank perturbations of structured matrices are established. A couple of simple examples provide natural and sometimes sharp bounds for the proposed conjectures. Mathematics Subject Classification (2000). Primary 12D10; Secondary 26C10, 30C10, 15A42, 15B05. Keywords. Sendov conjecture, Hausdorff distance, critical point, differentiator, variance, Chebyshev radius, Cauchy transform. 1. Introduction In 1958, while working as an assistant to Professor N. Obreshkov, Blagovest Sendov raised the following question. Assume that all zeros of a polynomial F with complex coefficients lie in the closed unit disk. Is it true that there exists a critical point in arXiv:1010.5167v2 [math.CV] 10 Jan 2011 every disk of radius one centered at a zero of F ? The conjecture was included in the 1967 book of research problems collected and edited by W. Hayman [31]. The This work was completed with the support of the American Institute of Mathematics, Palo Alto. D. Khavinson, M. Putinar and E. Saff also gratefully acknowledge the support by the National Science Foundation, through the grants DMS-0855597, DMS-1001071 and DMS-0808093, respec- tively. -
Notions of Positivity and the Geometry of Polynomials
Trends in Mathematics Notions of Positivity and the Geometry of Polynomials Bearbeitet von Petter Brändén, Mikael Passare, Mihai Putinar 1. Auflage 2011. Buch. XX, 403 S. Hardcover ISBN 978 3 0348 0141 6 Format (B x L): 15,5 x 23,5 cm Gewicht: 795 g Weitere Fachgebiete > Physik, Astronomie > Physik Allgemein > Theoretische Physik, Mathematische Physik schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, eBooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte. Inˆ noapte undeva mai e tot ce-a fost ¸si nu mai e, ce s-a mutat, ce s-a pierdut din timpul viu ˆın timpul mut. Inˆ Hades e – tot ce-a trecut. Din aheronticul¸inut t vin toate amintirile. Inˆ Hades e – tot ce-a trecut prierii ¸si iubirile. (In noapte undeva mai e, de Lucian Blaga) Lost in the night, somewhere, there is all that once was and no more is, what got lost, what was uprooted, from living time to time that’s muted. In Hades is – all that has passed. From Acheron, the river vast, all memories to us return. In Hades is – all that has passed the springtimes, and the loves we yearn. (Lost in the night, somewhere, there is by Lucian Blaga)1 Introduction This book is dedicated to the memory of Julius Borcea, visionary mathematician whose fervor and intensity left no one indifferent.