Jahrestagung Der Deutschen Mathematiker-Vereinigung Deutschen Der Jahrestagung Herausgegeben Von / Edited by by Edited / Von Herausgegeben

Total Page:16

File Type:pdf, Size:1020Kb

Jahrestagung Der Deutschen Mathematiker-Vereinigung Deutschen Der Jahrestagung Herausgegeben Von / Edited by by Edited / Von Herausgegeben 2015 of of of thethethe Hendrik Niehaus , in Hamburg, Germany Germany in Hamburg, in Hamburg, , , 2015 2015 2015 2015 & September 21 – 25 schen Mathematiker-Vereinigung 25. restagung der restagung bis Jahrestagung der Jahrestagung Deutschen Mathematiker-Vereinigung und Hansestadt Hamburg Freie 21. edited by / von herausgegeben Benedikt Löwe Annual Meeting Deutsche Mathematiker-Vereinigung Deutsche Mathematiker-Vereinigung September bis bis Hamburg, Hansestadt und Freie September September Hendrik Niehaus Hendrik Löwe Benedikt & 25. 21. 2015 Jahrestagung der Deutschen Mathematiker-Vereinigung Deutschen der Jahrestagung herausgegeben von / edited by by edited / von herausgegeben Programm Schedule Monday, 21 September 2015 Tuesday, 22 September 2015 Wednesday, 23 September 2015 Thursday, 24 September 2015 Friday, 25 September 2015 Jørgen Ellegaard Andersen Michael Eichmair Kathrin Bringmann Charles M. Elliott Minimal surfaces, isoperimetry, and non-negative Topological quantum fi eld theory 9.00 -10.00 Meromorphic Maass forms PDEs on evolving domains scalar curvature in asymptotically fl at manifolds in low dimensional topology Hörsaal A Hörsaal A Hörsaal A Hörsaal A 10.00 - 10.30 Coffee Break Coffee Break Coffee Break Coffee Break Minisymposia 1: Minisymposia 3: Minisymposia 5: Minisymposia 7: #1, #2, #4, #15, #17, #18, #2, #4, #6, #12, #15, #17, #3, #5, #6, #10, #12, #14, #3, #5, #7, #8, #9, #11, 10.30 - 12.30 #20, #27, #32, #35, #36, #20, #21, #22, #26, #27, #31, #16, #19, #22, #23, #24, #25, #14, #16, #19, #23, #24, #37, #39. #32, #34, #35, #36, #37. #26, #28, #31, #37, #38. #25, #29, #30, #33, #38. 12.30 - 14.00 Lunch Break Lunch Break Mittagsseminar Lunch Break Mathematik in Industrie Minisymposia 2: Minisymposia 4: und Gesellschaft Minisymposia 8: 14.00 - 15.00 #1, #2, #4, #13, #15, #17, #18, #2, #4, #10, #15, #17, #18, #20, #21, #3, #5, #7, #8, #9, #11, #14, #16, #20, #21, #27, #32, #35, #36. #22, #26, #27, #32, #34, #35, #36. #23, #24, #25, #29, #30, #33, #38. 15.00 - 15.15 Coffee Break Coffee Break Coffee Break Coffee Break 15.15 - 16.00 Karen Vogtmann Cycles in moduli spaces of graphs 16.00 - 16.15 Hörsaal A Opening Sections Sections Sections Herbert Spohn 16.15 -17.00 Hörsaal A Interacting diffusions in the Kardar-Parisi-Zhang universality class 17.00 - 17.15 Alessandra Carbone Hörsaal A One-dimensional and three-dimensional 17.15 - 17.45 Coffee Break Coffee Break Coffee Break Closing – Hörsaal A protein spaces and protein evolution 17.45- 18.00 Hörsaal A Simon Thomas Björn Sandstede Minisymposia 6: A descriptive view of infi nite Turing patterns: past and present #3, #5, #9, #10, #14, #16, #19, #22, dimensional unitary representations 18.00 - 18.45 Hörsaal A Hörsaal A #23, #24, #25, #26, #28, #29, #33, #38. 18.45 - 19.15 Reception 19.15 - 19.30 (funded by Springer-Verlag) Mitgliederversammlung der DMV Hörsaal M Öffentliche Podiumsdiskussion Senatsempfang (gemeinsam mit der Akademie der Conference Dinner 19.30 - 21.00 Rathaus der Freien und Hansestadt Wissenschaften in Hamburg) Mozartsäle Hamburg Hörsaal A Jahrestagung der Deutschen Mathematiker-Vereinigung Freie und Hansestadt Hamburg 21. bis 25. September 2015 herausgegeben von / edited by Benedikt Löwe & Hendrik Niehaus © 2015. Verein zur Ausrichtung von Tagungen am Fachbereich Mathematik der Universität Hamburg e.V. Printed by kleinkariert medien, Hamburg. Cover design by Katja Stüber, Hamburg. The editors acknowledge the permissions of the Universität Hamburg, Hamburg Marketing GmbH, iStock by Getty, the Städtische Museen Jena, the Bildarchiv des Mathematischen Forschungsinstituts Oberwolfach, the Universitätsarchiv Freiburg, and the Deutsches Museum to reproduce image material. Photo credits and copyright for the header pictures: iStock.com / Fitzer, iStock.com / mathess, UHH, UHH / Dichant, Hendrik Niehaus, Hendrik Niehaus. Grußwort des DMV-Präsidenten Sehr geehrte Damen und Herren, es ist mir eine besondere Freude, Sie zur Jahrestagung 2015 der Deutschen Mathematiker-Vereinigung an der Universität Ham- burg begrüßen zu können! Freuen Sie sich mit mir auf ein vielfältiges wissenschaftliches Programm mit mathematisch erst- klassigen Hauptvorträgen, mit zehn Sektionen und fast vier- zig Minisymposien, das den aktuellen Status quo mathemati- scher Forschung in ihrer ganzen inhaltlichen Breite wiedergeben wird. Dieses Programm wird ergänzt durch eine Podiumsdiskussion zur Frage der Mathematik-Anforderungen für Studienanfänger in den MINT-Fächern, durch ein Mittagsseminar zur Mathematik in Indus- trie und Gesellschaft und vieles mehr! Wenn Sie Mitglied der DMV sind, sollten Sie bitte auch unbedingt zur Mitgliederver- sammlung kommen. Sollten Sie kein Mitglied der DMV sein, so würde es mich freuen, wenn Sie die Begeisterung über die DMV-Jahrestagung zu einer Mitgliedschaft bewegen würde. Viel Freude an der Tagung wünscht Ihnen Ihr Volker Bach Präsident der Deutschen Mathematiker-Vereinigung iii Grußwort des Fachbereichs Mathematik der Universität Hamburg Liebe Teilnehmerinnen und Teilnehmer, im Namen des Fachbereichs Mathematik der Universität Hamburg begrüßen wir Sie ganz herzlich in der Freien und Hansestadt Hamburg zur diesjährigen Jahrestagung der Deutschen Mathematiker-Vereinigung (DMV). Für unseren Fachbereich ist es eine große Ehre, im Jahr des 125-jährigen Gründungsjubiläums der DMV deren Jahrestagung zum vierten Male nach den Jahren 1901, 1928 und 1979 in Hamburg auszurichten. Die Freie und Hansestadt Hamburg hat eine vergleichsweise junge Universität, deren Gründung auf das Jahr 1919 datiert. Stand die auf Handel ausgerichtete Hansemetropole der Gründung einer Universität noch im frühen zwanzigsten Jahrhundert skeptisch gegen- über, so schätzte sie doch schon lange vor der Universitätsgründung die Wissenschaften, insbesondere die für die Stadt so wichtige Mathematik. Bereits 1690 wurde mit der “Kunst- Rechnungs-liebenden Societät” in Hamburg eine wissenschaftliche Gesellschaft gegründet, die später in der heutigen Mathematischen Gesellschaft in Hamburg aufging—heute eine der ältesten wissenschaftlichen Gesellschaften in Deutschland. Nach der Gründung der Universität Hamburg entwickelte sich eine lebhafte und for- schungsstarke akademische Gemeinschaft in unserem Fach, die durch berühmte Namen wie Emil Artin, Lothar Collatz, Helmut Hasse, Erich Hecke, Erich Kähler, Ernst Witt und anderen vertreten wird. Wir freuen uns, dass die Hamburger Mathematik nichts von ihrer Anziehungskraft in der deutschen Forschungslandschaft verloren hat, wie die überaus große Zahl der Teilneh- merinnen und Teilnehmer bei dieser Jahrestagung deutlich zeigt. In diesem Programmheft bieten wir Ihnen sowohl historische Rückblicke und Erinne- rungen (zur Geschichte unserer Universität, zu 125 Jahren Geschichte der DMV, zu den drei bisherigen DMV-Jahrestagungen in Hamburg, und zum Hamburger Gymnasialprofes- sor Hermann Schubert), als auch praktische Informationen für die kommenden fünf Tage und natürlich Zusammenfassungen der fast fünfhundert Vorträge, die auf unserer Tagung gehalten werden. Wir freuen uns, Sie alle hier begrüßen zu dürfen und wünschen Ihnen eine erfolgreiche Tagung. Michael Hinze Benedikt Löwe Leiter des Fachbereichs Mathematik Vorsitzender des Programmkomitees v Inhaltsverzeichnis / Table of Contents Grußwort des DMV-Präsidenten iii Grußwort des Fachbereichs Mathematik der Universität Hamburg v Inhaltsverzeichnis / Table of Contents vii Die DMV-Jahrestagung 2015 in Hamburg 1 Podiumsdiskussion Wie viel Mathematik brauchen Studierende der MINT-Fächer? 10 Mittagsseminar Mathematik in Industrie und Gesellschaft . 12 Praktische Informationen / Practical Information 13 D. C. Thompson: τ vs. π. An art intervention at the crossroads of mathematics and culture 23 Geschichte der Universität Hamburg 27 R. Tobies: 125 Jahre DMV 31 Die ersten beiden Hamburger DMV-Jahresversammlungen 1901 und 1928 39 R. Tobies: Hermann Schubert, die DMV und Hamburg 51 E. Bönecke: Einige Erinnerungen an die DMV-Jahrestagung 1979 in Hamburg 55 Gemeinsames Literaturverzeichnis 58 Hauptvortragende / Keynote Speakers 63 Sektionen / Sections 73 Sektion 1: Algebra & Zahlentheorie / Section 1: Algebra & Number Theory . 73 Sektion 2: Differentialgeometrie, globale Analysis & Anwendungen / Section 2: Differential Geometry, Global Analysis, & Applications . 79 Sektion 3: Differentialgleichungen & Anwendungen / Section 3: Differential Equa- tions & Applications . 88 Sektion 4: Diskrete Mathematik / Section 4: Discrete Mathematics . 97 vii Sektion 5: Funktionalanalysis, Reelle & Komplexe Analysis / Section 5: Func- tional Analysis, Real & Complex Analysis . 101 Sektion 6: Geometrie & Topologie / Section 6: Geometry & Topology . 105 Sektion 7: Geschichte & Didaktik der Mathematik / Sektion 7: History of Mathe- matics & Mathematics Education . 109 Sektion 8: Logik & Theoretische Informatik / Section 8: Logic & Theoretical Computer Science . 116 Sektion 9: Numerik & Wissenschaftliches Rechnen / Section 9: Numerical Anal- ysis & Scientific Computing . 121 Sektion 10: Stochastik, Statistik & Finanzmathematik / Section 10: Stochastics, Statistics, & Financial Mathematics . 127 Minisymposien / Mini-Symposia 131 MS#1: Abiturstandards—Möglichkeiten, Chancen und Grenzen ihrer Umsetzung 131 MS#2: Algebraic Aspects of Cryptology . 132 MS#3: Algebraic Quantum Field Theory on Lorentzian Manifolds . 135 MS#4: Applied and Computational Harmonic Analysis . 139 MS#5: Computer Algebra and Applications . 144 MS#6: DGVFM-Minisymposium in Financial and Insurance Mathematics . 147 MS#7: Didactical aspects and functions of graphical
Loading...
Loading...
Loading...
Loading...
Loading...

253 pages remaining, click to load more.

Recommended publications
  • Sitzungsberichte Der Mathematisch- Physikalischen Klasse Der Bayerischen Akademie Der Wissenschaften München
    ZOBODAT - www.zobodat.at Zoologisch-Botanische Datenbank/Zoological-Botanical Database Digitale Literatur/Digital Literature Zeitschrift/Journal: Sitzungsberichte der mathematisch- physikalischen Klasse der Bayerischen Akademie der Wissenschaften München Jahr/Year: 1986 Band/Volume: 1985 Autor(en)/Author(s): Biermann Ludwig F. B., Grigull Ulrich Artikel/Article: Fünfzig Jahre Kepler-Kommission 50 Jahre Kepler- Kommission 23-31 BAYERISCHE AKADEMIE DER WISSENSCHAFTEN MATHEMATISCH-NATURWISSENSCHAFTLICHE KLASSE SITZUNGSBERICHTE JAHRGANG 1985 MÜNCHEN 1986 VERLAG DER BAYERISCHEN AKADEMIE DER WISSENSCHAFTEN In Kommission bei der C.H. Beck’schen Verlagsbuchhandlung München 50 Jahre Kepler-Kommission Ludwig F. B. Biermannt und Ulrich Grigull Vorgetragen auf der Gedenkfeier der Kepler-Kommission am 15. Juli 1985 Die Aktivitäten der Bayerischen Akademie der Wissenschaften zur Herausgabe der Werke von Johannes Kepler haben ihren Ursprung darin, daß das Akademiemitglied Walther von Dyck (*1856 in Mün- chen) sich mit Kepler zu beschäftigen begann, vermutlich auf Anre- gung seines Freundes Oskar von Miller. Schon Anfang desjahrhun- derts war Walther von Dyck von Oskar von Miller um einen Vor- trag über Johannes Kepler gebeten worden und hatte bei den Vorbe- reitungen dazu festgcstcllt, daß ein großer Teil der Schriften Keplers in der einzigen damals existierenden Ausgabe der Gesammelten Wer- ke - welche der württcmbcrgische Gelehrte Christian Frisch zwi- schen 1858 und 1871 besorgt hatte - nicht berücksichtigt war. Wal- ther von Dyck begann, Keplers Manuskripte systematisch zu sam- meln; als erstes Ergebnis erschienen 1910 unter den Abhandlungen der mathematisch-naturwissenschaftlichen Klasse unserer Akademie zwei wieder aufgefundene Prognostika auf diejahre 1604 und 1624, die Walther von Dyck am 5. November 1910 der Klasse vorlegte und die auch noch im gleichen Jahr gedruckt wurden.
    [Show full text]
  • Mathematicians Fleeing from Nazi Germany
    Mathematicians Fleeing from Nazi Germany Mathematicians Fleeing from Nazi Germany Individual Fates and Global Impact Reinhard Siegmund-Schultze princeton university press princeton and oxford Copyright 2009 © by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved Library of Congress Cataloging-in-Publication Data Siegmund-Schultze, R. (Reinhard) Mathematicians fleeing from Nazi Germany: individual fates and global impact / Reinhard Siegmund-Schultze. p. cm. Includes bibliographical references and index. ISBN 978-0-691-12593-0 (cloth) — ISBN 978-0-691-14041-4 (pbk.) 1. Mathematicians—Germany—History—20th century. 2. Mathematicians— United States—History—20th century. 3. Mathematicians—Germany—Biography. 4. Mathematicians—United States—Biography. 5. World War, 1939–1945— Refuges—Germany. 6. Germany—Emigration and immigration—History—1933–1945. 7. Germans—United States—History—20th century. 8. Immigrants—United States—History—20th century. 9. Mathematics—Germany—History—20th century. 10. Mathematics—United States—History—20th century. I. Title. QA27.G4S53 2008 510.09'04—dc22 2008048855 British Library Cataloging-in-Publication Data is available This book has been composed in Sabon Printed on acid-free paper. ∞ press.princeton.edu Printed in the United States of America 10 987654321 Contents List of Figures and Tables xiii Preface xvii Chapter 1 The Terms “German-Speaking Mathematician,” “Forced,” and“Voluntary Emigration” 1 Chapter 2 The Notion of “Mathematician” Plus Quantitative Figures on Persecution 13 Chapter 3 Early Emigration 30 3.1. The Push-Factor 32 3.2. The Pull-Factor 36 3.D.
    [Show full text]
  • Function Spaces Mikko Salo
    Function spaces Lecture notes, Fall 2008 Mikko Salo Department of Mathematics and Statistics University of Helsinki Contents Chapter 1. Introduction 1 Chapter 2. Interpolation theory 5 2.1. Classical results 5 2.2. Abstract interpolation 13 2.3. Real interpolation 16 2.4. Interpolation of Lp spaces 20 Chapter 3. Fractional Sobolev spaces, Besov and Triebel spaces 27 3.1. Fourier analysis 28 3.2. Fractional Sobolev spaces 33 3.3. Littlewood-Paley theory 39 3.4. Besov and Triebel spaces 44 3.5. H¨olderand Zygmund spaces 54 3.6. Embedding theorems 60 Bibliography 63 v CHAPTER 1 Introduction In mathematical analysis one deals with functions which are dif- ferentiable (such as continuously differentiable) or integrable (such as square integrable or Lp). It is often natural to combine the smoothness and integrability requirements, which leads one to introduce various spaces of functions. This course will give a brief introduction to certain function spaces which are commonly encountered in analysis. This will include H¨older, Lipschitz, Zygmund, Sobolev, Besov, and Triebel-Lizorkin type spaces. We will try to highlight typical uses of these spaces, and will also give an account of interpolation theory which is an important tool in their study. The first part of the course covered integer order Sobolev spaces in domains in Rn, following Evans [4, Chapter 5]. These lecture notes contain the second part of the course. Here the emphasis is on Sobolev type spaces where the smoothness index may be any real number. This second part of the course is more or less self-contained, in that we will use the first part mainly as motivation.
    [Show full text]
  • Matters of Gravity
    MATTERS OF GRAVITY The newsletter of the Division of Gravitational Physics of the American Physical Society Number 49 June 2017 Contents DGRAV News: we hear that . , by David Garfinkle ..................... 3 DGRAV student travel grants, by Beverly Berger .............. 4 Research Briefs: The Discovery of GW170104, by Jenne Driggers and Salvatore Vitale ... 5 Obituary: Remembering Vishu, by Naresh Dadhich and Bala Iyer ........... 8 Remembering Cecile DeWitt-Morette, by Yvonne Choquet-Bruhat ..... 13 arXiv:1706.06183v2 [gr-qc] 22 Jun 2017 Remembering Larry Shepley, by Richard Matzner and Mel Oakes ...... 15 Remembering Marcus Ansorg, by Bernd Br¨ugmannand Reinhard Meinel . 16 Conference Reports: EGM20, by Abhay Ashtekar ......................... 18 Editor David Garfinkle Department of Physics Oakland University Rochester, MI 48309 Phone: (248) 370-3411 Internet: garfinkl-at-oakland.edu WWW: http://www.oakland.edu/?id=10223&sid=249#garfinkle Associate Editor Greg Comer Department of Physics and Center for Fluids at All Scales, St. Louis University, St. Louis, MO 63103 Phone: (314) 977-8432 Internet: comergl-at-slu.edu WWW: http://www.slu.edu/colleges/AS/physics/profs/comer.html ISSN: 1527-3431 DISCLAIMER: The opinions expressed in the articles of this newsletter represent the views of the authors and are not necessarily the views of APS. The articles in this newsletter are not peer reviewed. 1 Editorial The next newsletter is due December 2017. This and all subsequent issues will be available on the web at https://files.oakland.edu/users/garfinkl/web/mog/ All issues before number 28 are available at http://www.phys.lsu.edu/mog Any ideas for topics that should be covered by the newsletter should be emailed to me, or Greg Comer, or the relevant correspondent.
    [Show full text]
  • Witt's Cancellation Theorem Seen As a Cancellation 1
    WITT'S CANCELLATION THEOREM SEEN AS A CANCELLATION SUNIL K. CHEBOLU, DAN MCQUILLAN, AND JAN´ MINA´ Cˇ Dedicated to the late Professor Amit Roy Abstract. Happy birthday to the Witt ring! The year 2017 marks the 80th anniversary of Witt's famous paper containing some key results, including the Witt cancellation theorem, which form the foundation for the algebraic theory of quadratic forms. We pay homage to this paper by presenting a transparent, algebraic proof of the Witt cancellation theorem, which itself is based on a cancellation. We also present an overview of some recent spectacular work which is still building on Witt's original creation of the algebraic theory of quadratic forms. 1. Introduction The algebraic theory of quadratic forms will soon celebrate its 80th birthday. Indeed, it was 1937 when Witt's pioneering paper [24] { a mere 14 pages { first introduced many beautiful results that we love so much today. These results form the foundation for the algebraic theory of quadratic forms. In particular they describe the construction of the Witt ring itself. Thus the cute little baby, \The algebraic theory of quadratic forms" was healthy and screaming with joy, making his father Ernst Witt very proud. Grandma Emmy Noether, Figure 1. Shortly after the birth of the Algebraic Theory of Quadratic Forms. had she still been alive, would have been so delighted to see this little tyke! 1 Almost right 1Emmy Noether's male Ph.D students, including Ernst Witt, were often referred to as \Noether's boys." The reader is encouraged to consult [6] to read more about her profound influence on the development of mathematics.
    [Show full text]
  • Banach Space Operators with a Bounded H∞ Functional Calculus
    J. Austral. Math. Soc. (Series A) 60 (1996), 51-89 BANACH SPACE OPERATORS WITH A BOUNDED H°° FUNCTIONAL CALCULUS - MICHAEL COWLING, IAN DOUST, ALAN MCINTOSH and ATSUSHIYAGI (Received 19 August 1993) Communicated by A. H. Dooley Abstract In this paper, we give a general definition for f(T) when T is a linear operator acting in a Banach space, whose spectrum lies within some sector, and which satisfies certain resolvent bounds, and when / is holomorphic on a larger sector. We also examine how certain properties of this functional calculus, such as the existence of a bounded H°° functional calculus, bounds on the imaginary powers, and square function estimates are related. In particular we show that, if T is acting in a reflexive Lp space, then T has a bounded H°° functional calculus if and only if both T and its dual satisfy square function estimates. Examples are given to show that some of the theorems that hold for operators in a Hilbert space do not extend to the general Banach space setting. 1991 Mathematics subject classification (Amer. Math. Soc): 47A60. 1. Introduction and notation Operators whose spectrum lies in some sector of the complex plane, and whose resolvents satisfy certain bounds, have been extensively studied, both in abstract settings and for their applications to differential equations. For example the m- accretive and m-sectorial operators studied in [12] fall into this class. An extensive list of examples of such operators may be found in [17], which also includes a good description of some of the applications: diffusion semigroups, Stokes' operators, etc.
    [Show full text]
  • Trace and Extension Theorems for Sobolev-Type Functions in Metric
    TRACE AND EXTENSION THEOREMS FOR SOBOLEV-TYPE FUNCTIONS IN METRIC SPACES LUKÁŠ MALÝ Abstract. Trace classes of Sobolev-type functions in metric spaces are subject of this paper. In particular, functions on domains whose boundary has an upper codimension-θ bound are consid- ered. Based on a Poincaré inequality, existence of a Borel measurable trace is proven whenever the power of integrability of the “gradient” exceeds θ. The trace T is shown to be a compact operator mapping a Sobolev-type space on a domain into a Besov space on the boundary. Sucient condi- tions for T to be surjective are found and counterexamples showing that surjectivity may fail are also provided. The case when the exponent of integrability of the “gradient” is equal to θ, i.e., the codimension of the boundary, is also discussed. Under some additional assumptions, the trace lies in Lθ on the boundary then. Essential sharpness of these extra assumptions is illustrated by an example. 1. Introduction and Overview Over the past two decades, analysis in metric measure spaces (and non-linear potential theory, in particular) has attracteda lot of attention, e.g., [3, 4, 14, 15, 21, 28]. See also [19, Chapter 22] and referencestherein. The metricspace setting provides a wide framework to study partial dierential equations and, specically, boundary value problems. These seek to nd solutions to an equation in a domain, subject to a prescribed boundary condition. Most thoroughly studied problems deal with the Dirichlet boundary condition, where a trace of the solution is prescribed, and with the Neumann condition, where the normal derivative of the solution at the boundary is given.
    [Show full text]
  • Section I.9. Free Groups, Free Products, and Generators and Relations
    I.9. Free Groups, Free Products, and Generators and Relations 1 Section I.9. Free Groups, Free Products, and Generators and Relations Note. This section includes material covered in Fraleigh’s Sections VII.39 and VII.40. We define a free group on a set and show (in Theorem I.9.2) that this idea of “free” is consistent with the idea of “free on a set” in the setting of a concrete category (see Definition I.7.7). We also define generators and relations in a group presentation. Note. To define a free group F on a set X, we will first define “words” on the set, have a way to reduce these words, define a method of combining words (this com- bination will be the binary operation in the free group), and then give a reduction of the combined words. The free group will have the reduced words as its elements and the combination as the binary operation. If set X = ∅ then the free group on X is F = hei. Definition. Let X be a nonempty set. Define set X−1 to be disjoint from X such that |X| = |X−1|. Choose a bijection from X to X−1 and denote the image of x ∈ X as x−1. Introduce the symbol “1” (with X and X−1 not containing 1). A −1 word on X is a sequence (a1, a2,...) with ai ∈ X ∪ X ∪ {1} for i ∈ N such that for some n ∈ N we have ak = 1 for all k ≥ n. The sequence (1, 1,...) is the empty word which we will also sometimes denote as 1.
    [Show full text]
  • Quadratic Forms and Their Applications
    Quadratic Forms and Their Applications Proceedings of the Conference on Quadratic Forms and Their Applications July 5{9, 1999 University College Dublin Eva Bayer-Fluckiger David Lewis Andrew Ranicki Editors Published as Contemporary Mathematics 272, A.M.S. (2000) vii Contents Preface ix Conference lectures x Conference participants xii Conference photo xiv Galois cohomology of the classical groups Eva Bayer-Fluckiger 1 Symplectic lattices Anne-Marie Berge¶ 9 Universal quadratic forms and the ¯fteen theorem J.H. Conway 23 On the Conway-Schneeberger ¯fteen theorem Manjul Bhargava 27 On trace forms and the Burnside ring Martin Epkenhans 39 Equivariant Brauer groups A. FrohlichÄ and C.T.C. Wall 57 Isotropy of quadratic forms and ¯eld invariants Detlev W. Hoffmann 73 Quadratic forms with absolutely maximal splitting Oleg Izhboldin and Alexander Vishik 103 2-regularity and reversibility of quadratic mappings Alexey F. Izmailov 127 Quadratic forms in knot theory C. Kearton 135 Biography of Ernst Witt (1911{1991) Ina Kersten 155 viii Generic splitting towers and generic splitting preparation of quadratic forms Manfred Knebusch and Ulf Rehmann 173 Local densities of hermitian forms Maurice Mischler 201 Notes towards a constructive proof of Hilbert's theorem on ternary quartics Victoria Powers and Bruce Reznick 209 On the history of the algebraic theory of quadratic forms Winfried Scharlau 229 Local fundamental classes derived from higher K-groups: III Victor P. Snaith 261 Hilbert's theorem on positive ternary quartics Richard G. Swan 287 Quadratic forms and normal surface singularities C.T.C. Wall 293 ix Preface These are the proceedings of the conference on \Quadratic Forms And Their Applications" which was held at University College Dublin from 5th to 9th July, 1999.
    [Show full text]
  • QUANTIZATIONS and SYMBOLIC CALCULUS OVER the P-ADIC NUMBERS
    Ann. Inst. Fourier, Grenoble 43, 4 (1993), 997-1053 QUANTIZATIONS AND SYMBOLIC CALCULUS OVER THE p-ADIC NUMBERS by Shai HARAN INTRODUCTION We shall be concerned with functions / : VQ —^ C, defined in some vector space Vo OYer the p-adic numbers Qp and taking values in the complex numbers C. One of the most basic problems encountered when trying to imitate the classical theory — where the domain VQ is a vector space over R or C — is the lack of derivatives. Indeed, the derivation 9/Qx is nothing but T~^xF^ where T is the Fourier transform, and «a;» is multiplication by the function x which is an additive homomorphism from VQ to C; and there are no such homomorphisms from Vo to C when VQ is a vector space over Qp. This problem repeatedly makes its appearance in various disguises; for example, given a unitary representation of a p-adic analytic group on a Hilbert space, one cannot associate with it the derived representation of a p-adic Lie algebra. From a different perspective, the derivatives {Q/Qx^ correspond to the extra poles of the oo-component of the zeta function, while the p-components have a unique pole. There are thus no differential operators over Qp. But as we will show in this paper, there is a meaningful theory of pseudodifferential operators over the p-adics, which parallels the classical theory over the real numbers R. In fact, the theory over Qp is better behaved than the one over R, in as much as in all estimates the numbers 2 = [C : R] for the reals can be replaced by oo = [Qp : Qp] for the p-adics, and one encounters here the phenomenon expounded in [15], [16].
    [Show full text]
  • Contributions to the History of Number Theory in the 20Th Century Author
    Peter Roquette, Oberwolfach, March 2006 Peter Roquette Contributions to the History of Number Theory in the 20th Century Author: Peter Roquette Ruprecht-Karls-Universität Heidelberg Mathematisches Institut Im Neuenheimer Feld 288 69120 Heidelberg Germany E-mail: roquette@uni-hd.de 2010 Mathematics Subject Classification (primary; secondary): 01-02, 03-03, 11-03, 12-03 , 16-03, 20-03; 01A60, 01A70, 01A75, 11E04, 11E88, 11R18 11R37, 11U10 ISBN 978-3-03719-113-2 The Swiss National Library lists this publication in The Swiss Book, the Swiss national bibliography, and the detailed bibliographic data are available on the Internet at http://www.helveticat.ch. 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, broad- casting, 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. © 2013 European Mathematical Society Contact address: European Mathematical Society Publishing House Seminar for Applied Mathematics ETH-Zentrum SEW A27 CH-8092 Zürich Switzerland Phone: +41 (0)44 632 34 36 Email: info@ems-ph.org Homepage: www.ems-ph.org Typeset using the author’s TEX files: I. Zimmermann, Freiburg Printing and binding: Beltz Bad Langensalza GmbH, Bad Langensalza, Germany ∞ Printed on acid free paper 9 8 7 6 5 4 3 2 1 To my friend Günther Frei who introduced me to and kindled my interest in the history of number theory Preface This volume contains my articles on the history of number theory except those which are already included in my “Collected Papers”.
    [Show full text]
  • The Chaning Face of Science and Technology in the Ehrensaal of The
    PREPRINT 13 Lisa Kirch The Changing Face of Science and Technology in the Ehrensaal of the Deutsches Museum, 1903–1955 The Changing Face of Science and Technology in the Ehrensaal of the Deutsches Museum, 1903–1955 Deutsches Museum Preprint Edited by Deutsches Museum Issue 13 Lisa Kirch received her Ph. D. in art history (University of Texas at Austin, 2003) with a dissertation on the portraits of Elector Palatine Ottheinrich (1502–1559). In collaboration with Andreas Kühne (LMU) she has published articles on portraits of the Herschel family and on the presentation and conservation of modern art. Her publications on visual and material culture in early-modern Germany appear under Miriam Hall Kirch. She is Associate Professor in the Art Department of the University of North Alabama. Lisa Kirch The Changing Face of Science and Technology in the Ehrensaal of the Deutsches Museum, 1903–1955 Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet unter http://dnb.d-nb.de abrufbar. Lisa Kirch, “The Changing Face of Science and Technology in the Ehrensaal of the Deutsches Museum, 1903–1955” © 2017 of the present edition: MV-Wissenschaft MV-Wissenschaft is published by readbox publishing GmbH, Dortmund http://unipress.readbox.net/ © Deutsches Museum Verlag All rights reserved Editor: Dorothee Messerschmid Layout and Design: Jutta Esser Cover illustration: Draft of the Lilienthal glider, 1895
    [Show full text]