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Mathematics People
Mathematics People symmetric spaces, L²-cohomology, arithmetic groups, and MacPherson Awarded Hopf the Langlands program. The list is by far not complete, and Prize we try only to give a representative selection of his contri- bution to mathematics. He influenced a whole generation Robert MacPherson of the Institute for Advanced Study of mathematicians by giving them new tools to attack has been chosen the first winner of the Heinz Hopf Prize difficult problems and teaching them novel geometric, given by ETH Zurich for outstanding scientific work in the topological, and algebraic ways of thinking.” field of pure mathematics. MacPherson, a leading expert Robert MacPherson was born in 1944 in Lakewood, in singularities, delivered the Heinz Hopf Lectures, titled Ohio. He received his B.A. from Swarthmore College in “How Nature Tiles Space”, in October 2009. The prize also 1966 and his Ph.D. from Harvard University in 1970. He carries a cash award of 30,000 Swiss francs, approximately taught at Brown University from 1970 to 1987 and at equal to US$30,000. the Massachusetts Institute of Technology from 1987 to The following quotation was taken from a tribute to 1994. He has been at the Institute for Advanced Study in MacPherson by Gisbert Wüstholz of ETH Zurich: “Singu- Princeton since 1994. His work has introduced radically larities can be studied in different ways using analysis, new approaches to the topology of singular spaces and or you can regard them as geometric phenomena. For the promoted investigations across a great spectrum of math- latter, their study demands a deep geometric intuition ematics. -
Bibliography
Bibliography [AK98] V. I. Arnold and B. A. Khesin, Topological methods in hydrodynamics, Springer- Verlag, New York, 1998. [AL65] Holt Ashley and Marten Landahl, Aerodynamics of wings and bodies, Addison- Wesley, Reading, MA, 1965, Section 2-7. [Alt55] M. Altman, A generalization of Newton's method, Bulletin de l'academie Polonaise des sciences III (1955), no. 4, 189{193, Cl.III. [Arm83] M.A. Armstrong, Basic topology, Springer-Verlag, New York, 1983. [Bat10] H. Bateman, The transformation of the electrodynamical equations, Proc. Lond. Math. Soc., II, vol. 8, 1910, pp. 223{264. [BB69] N. Balabanian and T.A. Bickart, Electrical network theory, John Wiley, New York, 1969. [BLG70] N. N. Balasubramanian, J. W. Lynn, and D. P. Sen Gupta, Differential forms on electromagnetic networks, Butterworths, London, 1970. [Bos81] A. Bossavit, On the numerical analysis of eddy-current problems, Computer Methods in Applied Mechanics and Engineering 27 (1981), 303{318. [Bos82] A. Bossavit, On finite elements for the electricity equation, The Mathematics of Fi- nite Elements and Applications IV (MAFELAP 81) (J.R. Whiteman, ed.), Academic Press, 1982, pp. 85{91. [Bos98] , Computational electromagnetism: Variational formulations, complementar- ity, edge elements, Academic Press, San Diego, 1998. [Bra66] F.H. Branin, The algebraic-topological basis for network analogies and the vector cal- culus, Proc. Symp. Generalised Networks, Microwave Research, Institute Symposium Series, vol. 16, Polytechnic Institute of Brooklyn, April 1966, pp. 453{491. [Bra77] , The network concept as a unifying principle in engineering and physical sciences, Problem Analysis in Science and Engineering (K. Husseyin F.H. Branin Jr., ed.), Academic Press, New York, 1977. -
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. -
Differential Geometry in the Large Seminar Lectures New York University 1946 and Stanford University 1956 Series: Lecture Notes in Mathematics
springer.com Heinz Hopf Differential Geometry in the Large Seminar Lectures New York University 1946 and Stanford University 1956 Series: Lecture Notes in Mathematics These notes consist of two parts: Selected in York 1) Geometry, New 1946, Topics University Notes Peter Lax. by Differential in the 2) Lectures on Stanford Geometry Large, 1956, Notes J. W. University by Gray. are here with no essential They reproduced change. Heinz was a mathematician who mathema- Hopf recognized important tical ideas and new mathematical cases. In the phenomena through special the central idea the of a or difficulty problem simplest background is becomes clear. in this fashion a crystal Doing geometry usually lead serious allows this to to - joy. Hopf's great insight approach for most of the in these notes have become the st- thematics, topics I will to mention a of further try ting-points important developments. few. It is clear from these notes that laid the on Hopf emphasis po- differential 2nd ed. 1989, VIII, 192 p. Most of the results in smooth differ- hedral geometry. whose is both t1al have understanding geometry polyhedral counterparts, works I wish to mention and recent important challenging. Printed book Among those of Robert on which is much in the Connelly rigidity, very spirit R. and in - of these notes (cf. Connelly, Conjectures questions open International of Mathematicians, H- of Softcover gidity, Proceedings Congress sinki vol. 1, 407-414) 1978, . 29,95 € | £26.99 | $49.95 [1]32,05 € (D) | 32,95 € (A) | CHF 43,04 eBook 24,60 € | £20.99 | $34.99 [2]24,60 € (D) | 24,60 € (A) | CHF 34,00 Available from your library or springer.com/shop MyCopy [3] Printed eBook for just € | $ 24.99 springer.com/mycopy Error[en_EN | Export.Bookseller. -
Quelques Souvenirs Des Années 1925-1950 Cahiers Du Séminaire D’Histoire Des Mathématiques 1Re Série, Tome 1 (1980), P
CAHIERS DU SÉMINAIRE D’HISTOIRE DES MATHÉMATIQUES GEORGES DE RHAM Quelques souvenirs des années 1925-1950 Cahiers du séminaire d’histoire des mathématiques 1re série, tome 1 (1980), p. 19-36 <http://www.numdam.org/item?id=CSHM_1980__1__19_0> © Cahiers du séminaire d’histoire des mathématiques, 1980, tous droits réservés. L’accès aux archives de la revue « Cahiers du séminaire d’histoire des mathématiques » im- plique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pé- nale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ - 19 - QUELQUES SOUVENIRS DES ANNEES 1925-1950 par Georges de RHAM Arrivé à la fin de ma carrière, je pense à son début. C’est dans ma année 1. en 1924, que j’ai décidé de me lancer dans les mathématiques. En 1921, ayant le bachot classique, avec latin et grec, attiré par la philosophie, j’hésitais d’entrer à la Facul- té des Lettres. Mais finalement je me décidai pour la Faculté des Sciences, avec à mon programme l’étude de la Chimie, de la Physique et surtout, pour finir, la Biologie. Je ne songeais pas aux Mathématiques, qui me semblaient un domaine fermé où je ne pourrais rien faire. Pourtant, pour comprendre des questions de Physique, je suis amené à ouvrir des livres de Mathématiques supérieures. J’entrevois qu’il y a là un domaine immense, qui ex- cité ma curiosité et m’intéresse à tel point qu’après cinq semestres à l’Université, j’ abandonne la Biologie pour aborder résolument les Mathématiques. -
Urs Stammbach, ETH-Zürich List of Publications A. Papers
Urs Stammbach, ETH-Z¨urich List of Publications A. Papers [1] Anwendungen der Homologietheorie der Gruppen auf Zentralreihen und auf Invari- anten von Pr¨asentierungen, Math. Z. 94 (1966), 155 - 177. [2] (with M.-A. Knus) Anwendungen der Homologietheorie der Liealgebren auf Zentral- reihen und auf Pr¨asentierungen, Comment. Math. Helv. 42 (1967), 297 - 306. [3] Ein neuer Beweis eines Satzes von Magnus, Proc. Cambridge Phil. Soc. 63 (1967), 929 - 930. [4] Uber¨ freie Untergruppen gegebener Gruppen, Comment. Math. Helv. 43 (1968), 132 - 136. [5] (with B. Eckmann) Homologie et diff´erentielles. Suites exactes, C. R. Acad. Sci. Paris 265 (1967), 11 - 13. [6] (with B. Eckmann) Homologie et diff´erentielles. Basses dimensions, cas sp´eciaux,C. R. Acad. Sci. Paris 265 (1967), 46 - 48. [7] (with B. Eckmann) On exact sequences in the homology of groups and algebras, Illinois J. Math. 14 (1970), 205 - 215. [8] On the weak homological dimension of the group algebra of solvable groups, J. London Math. Soc. (2) 2 (1970), 567 - 570. [9] Homological methods in group varieties, Comment. Math. Helv. 45 (1970), 287 - 298. [10] Varietal homology and parafree groups, Math. Z. 128 (1972), 153 - 167. [11] (with B. Eckmann and P.J. Hilton) On the homology theory of central group exten- sions. I. The commutator map and stem extensions, Comment. Math. Helv. 47 (1972), 102 -122. [12] (with B. Eckmann and P.J. Hilton) On the homology theory of central group exten- sions. II. The exact sequence in the general case, Comment. Math. Helv. 47 (1972), 171 -178. [13] (with B. Eckmann and P.J. -
Constrained Optimization on Manifolds
Constrained Optimization on Manifolds Von der Universit¨atBayreuth zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung von Juli´anOrtiz aus Bogot´a 1. Gutachter: Prof. Dr. Anton Schiela 2. Gutachter: Prof. Dr. Oliver Sander 3. Gutachter: Prof. Dr. Lars Gr¨une Tag der Einreichung: 23.07.2020 Tag des Kolloquiums: 26.11.2020 Zusammenfassung Optimierungsprobleme sind Bestandteil vieler mathematischer Anwendungen. Die herausfordernd- sten Optimierungsprobleme ergeben sich dabei, wenn hoch nichtlineare Probleme gel¨ostwerden m¨ussen. Daher ist es von Vorteil, gegebene nichtlineare Strukturen zu nutzen, wof¨urdie Op- timierung auf nichtlinearen Mannigfaltigkeiten einen geeigneten Rahmen bietet. Es ergeben sich zahlreiche Anwendungsf¨alle,zum Beispiel bei nichtlinearen Problemen der Linearen Algebra, bei der nichtlinearen Mechanik etc. Im Fall der nichtlinearen Mechanik ist es das Ziel, Spezifika der Struktur zu erhalten, wie beispielsweise Orientierung, Inkompressibilit¨atoder Nicht-Ausdehnbarkeit, wie es bei elastischen St¨aben der Fall ist. Außerdem k¨onnensich zus¨atzliche Nebenbedingungen ergeben, wie im wichtigen Fall der Optimalsteuerungsprobleme. Daher sind f¨urdie L¨osungsolcher Probleme neue geometrische Tools und Algorithmen n¨otig. In dieser Arbeit werden Optimierungsprobleme auf Mannigfaltigkeiten und die Konstruktion von Algorithmen f¨urihre numerische L¨osungbehandelt. In einer abstrakten Formulierung soll eine reelle Funktion auf einer Mannigfaltigkeit minimiert werden, mit der Nebenbedingung -
Jt3(S\ H. Hopf, W.K. Clifford, F. Klein
CHAPTER 20 jt3(S\ H. Hopf, W.K. Clifford, F. Klein H. Samelson* Department of Mathematics, Stanford University, Stanford, CA 94305, USA E-mail: [email protected] In 1931 there appeared the seminal paper [2] by Heinz Hopf, in which he showed that 7t2>{S^) (the third homotopy group of the two-sphere S^) is nontrivial, or more specifically that it contains an element of order oo. (His language was different. Homotopy groups had not been defined yet; E. Czech introduced them at the 1932 Congress in Zurich. Interest ingly enough, both Paul Alexandroff and Hopf persuaded him not to continue with these groups. They had different reasons for considering them as not fruitful; the one because they are Abehan, and the other (if I remember right) because there is no mechanism, like chains say, to compute them. It was not until 1936 that W. Hurewicz rediscovered them and made them respectable by proving substantial theorems with and about them.) There are two parts to the paper: The first one is the definition of what now is called the Hopf invariant and the proof of its homotopy invariance. The second consists in the presentation of an example of a map from S^ to S^ that has Hopf invariant 1 and thus represents an element of infinite order of 713(5^); it is what is now called the Hopf fibration; the inverse images of the points of S^ are great circles of S^. Taking S^ as the unit-sphere ki 1^ + k2p = 1 in C^, these circles are the intersections of S^ with the various complex lines through the origin. -
A Treatise on Quantum Clifford Algebras Contents
A Treatise on Quantum Clifford Algebras Habilitationsschrift Dr. Bertfried Fauser arXiv:math/0202059v1 [math.QA] 7 Feb 2002 Universitat¨ Konstanz Fachbereich Physik Fach M 678 78457 Konstanz January 25, 2002 To Dorothea Ida and Rudolf Eugen Fauser BERTFRIED FAUSER —UNIVERSITY OF KONSTANZ I ABSTRACT: Quantum Clifford Algebras (QCA), i.e. Clifford Hopf gebras based on bilinear forms of arbitrary symmetry, are treated in a broad sense. Five al- ternative constructions of QCAs are exhibited. Grade free Hopf gebraic product formulas are derived for meet and join of Graßmann-Cayley algebras including co-meet and co-join for Graßmann-Cayley co-gebras which are very efficient and may be used in Robotics, left and right contractions, left and right co-contractions, Clifford and co-Clifford products, etc. The Chevalley deformation, using a Clif- ford map, arises as a special case. We discuss Hopf algebra versus Hopf gebra, the latter emerging naturally from a bi-convolution. Antipode and crossing are consequences of the product and co-product structure tensors and not subjectable to a choice. A frequently used Kuperberg lemma is revisited necessitating the def- inition of non-local products and interacting Hopf gebras which are generically non-perturbative. A ‘spinorial’ generalization of the antipode is given. The non- existence of non-trivial integrals in low-dimensional Clifford co-gebras is shown. Generalized cliffordization is discussed which is based on non-exponentially gen- erated bilinear forms in general resulting in non unital, non-associative products. Reasonable assumptions lead to bilinear forms based on 2-cocycles. Cliffordiza- tion is used to derive time- and normal-ordered generating functionals for the Schwinger-Dyson hierarchies of non-linear spinor field theory and spinor electro- dynamics. -
Linear Functional Analysis
Linear Functional Analysis Joan Cerdà Graduate Studies in Mathematics Volume 116 American Mathematical Society Real Sociedad Matemática Española Linear Functional Analysis Linear Functional Analysis Joan Cerdà Graduate Studies in Mathematics Volume 116 American Mathematical Society Providence, Rhode Island Real Sociedad Matemática Española Madrid, Spain Editorial Board of Graduate Studies in Mathematics David Cox (Chair) Rafe Mazzeo Martin Scharlemann Gigliola Staffilani Editorial Committee of the Real Sociedad Matem´atica Espa˜nola Guillermo P. Curbera, Director Luis Al´ıas Alberto Elduque Emilio Carrizosa Rosa Mar´ıa Mir´o Bernardo Cascales Pablo Pedregal Javier Duoandikoetxea Juan Soler 2010 Mathematics Subject Classification. Primary 46–01; Secondary 46Axx, 46Bxx, 46Exx, 46Fxx, 46Jxx, 47B15. For additional information and updates on this book, visit www.ams.org/bookpages/gsm-116 Library of Congress Cataloging-in-Publication Data Cerd`a, Joan, 1942– Linear functional analysis / Joan Cerd`a. p. cm. — (Graduate studies in mathematics ; v. 116) Includes bibliographical references and index. ISBN 978-0-8218-5115-9 (alk. paper) 1. Functional analysis. I. Title. QA321.C47 2010 515.7—dc22 2010006449 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294 USA. -
Annual Report Academic Year 2009/10
Annual Report Academic Year 2009/10 This report contains information on the Swiss Doctoral Program in Mathematics. It covers the period of the academic year 2009/10, with a preview of the following academic year. To benefit from the hyperlinks, please use the online version on www.math.ch/dp. Extended Table of Contents page 1 Welcome: A brief description of the Doctoral Program page 2 Objectives: Intention and aims of the Doctoral Program page 3 Neighboring Schools: The partners of the Doctoral Program page 4 Spectrum of Activities: Overview of the character of activities of the Doctoral Program page 6 Responsibilities of the Committee: The administration of the Doctoral Program page 7 Directors: The two directors of the Doctoral Program and a PhD student representative page 8 Senior Committee Members and Junior Committee Members: The lists of senior and junior representatives of each university page 9 Secretary: The secretary of the Doctoral Program page 10 Enrollment: Terms and conditions for the participation in the Doctoral Program page 11 Scoring: Description of the scoring system page 12 Application Form: Online application form for students page 13 Registration Form: Online registration form for research groups page 14 Validation: Description of the validation procedure page 15 Validation Form: The validation form for students page 16 Reimbursement: Terms and conditions for reimbursement of participation costs page 17 Reimbursement Form: The reimbursement form for students page 18 Reporting: Description of the annual reporting system -
Georges De Rham 1903--1990
Georges de Rham 1903{1990 This is an English translation of the obituary notice by Beno Eckmann, appearing under the same title in Elemente der Mathematik 47(3) 118{122 (1992) (in German).∗ Original c 1992 Birkh¨auserVerlag and available at <http://eudml.org/doc/141534>. The news of the passing of Georges de Rham on 8 October 1990 has by now surely reached and moved all in the mathematical community. This journal would like to bid him farewell with the following communication. He was one of the important figures of mathematics in our century, his name and work belong to its enduring legacy, and the influence of his ideas on its development has by no means been exhausted yet. He was close to Elemente der Mathematik, which is broadly aimed at both instructors and students, and indeed for many years was among its contributors. Everything that was connected with teaching lay as close to his heart as research did. He was in the habit of saying, \Teaching, the conveying of essentials, making the beautiful intelligible and evident, that is what gives me joy; and instruction is always accompanied by interpretation." arXiv:1611.03806v1 [math.HO] 11 Nov 2016 He understood how to enlighten, in an unassuming yet memorable fashion, students at all levels about mathematics; perhaps they could unconsciously sense what a great mathematical power- house was at work here. The closer to him one became, whether as a novice or as a colleague, the more one was impressed by his personality: by his|there is no other way to say it—refined, yet not distant, bearing; by his charm, which came from the heart; by his unyielding straightforwardness and intensity; by his warmhearted friendship, loyalty, and readiness to help.