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Nikolay Luzin, His Students, Adversaries, and Defenders (Notes
Nikolay Luzin, his students, adversaries, and defenders (notes on the history of Moscow mathematics, 1914-1936) Yury Neretin This is historical-mathematical and historical notes on Moscow mathematics 1914-1936. Nikolay Luzin was a central figure of that time. Pavel Alexandroff, Nina Bari, Alexandr Khinchin, Andrey Kolmogorov, Mikhail Lavrentiev, Lazar Lyusternik, Dmitry Menshov, Petr Novikov, Lev Sсhnirelman, Mikhail Suslin, and Pavel Urysohn were his students. We discuss the time of the great intellectual influence of Luzin (1915-1924), the time of decay of his school (1922-1930), a moment of his administrative power (1934-1936), and his fall in July 1936. But the thing which served as a source of Luzin’s inner drama turned out to be a source of his subsequent fame... Lazar Lyusternik [351] Il est temps que je m’arr ete: voici que je dis, ce que j’ai d´eclar´e, et avec raison, ˆetre inutile `adire. Henri Lebesgue, Preface to Luzin’s book, Leˇcons sur les ensembles analytiques et leurs applications, [288] Прошло сто лет и что ж осталось От сильных, гордых сих мужей, Столь полных волею страстей? Их поколенье миновалось Alexandr Pushkin ’Poltava’ There is a common idea that a life of Nikolay Luzin can be a topic of a Shakespeare drama. I am agree with this sentence but I am extremely far from an intention to realize this idea. The present text is an impassive historical-mathematical and historical investigation of Moscow mathematics of that time. On the other hand, this is more a story of its initiation and turning moments than a history of achievements. -
Twenty Female Mathematicians Hollis Williams
Twenty Female Mathematicians Hollis Williams Acknowledgements The author would like to thank Alba Carballo González for support and encouragement. 1 Table of Contents Sofia Kovalevskaya ................................................................................................................................. 4 Emmy Noether ..................................................................................................................................... 16 Mary Cartwright ................................................................................................................................... 26 Julia Robinson ....................................................................................................................................... 36 Olga Ladyzhenskaya ............................................................................................................................. 46 Yvonne Choquet-Bruhat ....................................................................................................................... 56 Olga Oleinik .......................................................................................................................................... 67 Charlotte Fischer .................................................................................................................................. 77 Karen Uhlenbeck .................................................................................................................................. 87 Krystyna Kuperberg ............................................................................................................................. -
Chapter 4 X.Pdf
CHAPTER 4 ANALYSIS OF THE GOVERNING EQUATIONS 4.1 INTRODUCTION The mathematical nature of the systems of governing equations deduced in Chapters 2 and 3 is investigated in this chapter. The systems of PDEs that express the quasi-equilibrium approximation are studied in greater depth. The analysis is especially important for the systems whose solutions are likely to feature discontinuities, as a result of strong gradients growing steeper, or because the initial data is already discontinuous. The geomorphic shallow-water flows, such as the dam-break flow considered in Chapter 3, are the paradigmatic example of flows for which discontinuities arise fundamentally because of the initial conditions. Laboratory experiments show that, in the first instants of a sudden collapse of a dam, vertical accelerations are strong and a bore is formed, either through the breaking of a wave (Stansby et al. 1998) or due to the incorporation of bed material (Capart 2000, Leal et al. 2002). Intense erosion occurs in the vicinity of the dam and a highly saturated wave front is likely to form at ttt≡≈0 4 , thg00= , where h0 is the initial water depth in the reservoir. The saturated wave front can be seen forming in figure 3.1(a). Unlike the debris flow resulting from avalanches or lahars, the saturated front is followed by a sheet-flow similar to that 303 encountered in surf or swash zones (Asano 1995), as seen in figures 3.2(b) and (c). The intensity of the sediment transport decreases in the upstream direction as the flow velocities approach fluvial values. -
On the Iwasawa Invariants of Kato's Zeta Elements for Modular Forms
ON THE IWASAWA INVARIANTS OF KATO’S ZETA ELEMENTS FOR MODULAR FORMS CHAN-HO KIM, JAEHOON LEE, AND GAUTIER PONSINET Abstract. We study the behavior of the Iwasawa invariants of the Iwasawa modules which appear in Kato’s main conjecture without p-adic L-functions under congruences. It general- izes the work of Greenberg–Vatsal, Emerton–Pollack–Weston, B.D. Kim, Greenberg–Iovita– Pollack, and one of us simultaneously. As a consequence, we establish the propagation of Kato’s main conjecture for modular forms of higher weight at arbitrary good prime under the assumption on the mod p non-vanishing of Kato’s zeta elements. The application to the ± and ♯/♭-Iwasawa theory for modular forms is also discussed. Contents 1. Introduction 1 2. Main results and applications 6 3. “Prime-to-p local” Iwasawa theory 8 4. The zeta element side 11 5. The H2-side 16 6. The invariance of λ-invariants 18 7. Beyond the Fontaine–Laffaille range: the semi-stable ordinary case 19 Acknowledgement 21 References 21 1. Introduction 1.1. Overview. In Iwasawa theory for elliptic curves and modular forms, the techniques of congruences of modular forms has played important roles. Especially, in their ground-breaking work [GV00], Greenberg and Vatsal observed that both algebraic and analytic Iwasawa in- variants of elliptic curves with good ordinary reduction over the cyclotomic Zp-extension Q∞ of Q can be described in terms of the information of the residual representations and the local arXiv:1909.01764v2 [math.NT] 29 Nov 2019 behavior at bad reduction primes under the µ = 0 assumption. -
Arxiv:1806.02470V2 [Hep-Th] 3 Feb 2020 in Particular, Topology of 4-Manifolds and Vertex Operator Algebra
VOA[M4] Boris Feigin and Sergei Gukov Abstract. We take a peek at a general program that associates vertex (or, chiral) algebras to smooth 4-manifolds in such a way that operations on al- gebras mirror gluing operations on 4-manifolds and, furthermore, equivalent constructions of 4-manifolds give rise to equivalences (dualities) of the corre- sponding algebras. Contents 1. Introduction 1 2. Gluing via extensions: Toric M4 8 3. Operations and relations 16 4. Vertex algebras and trisections 25 5. Modules and knotted surfaces 30 6. Gluing via BRST reduction 33 7. Associated variety of VOA[M4] 36 References 37 1. Introduction The main goal of this paper is to blaze new trails between topology and algebra, arXiv:1806.02470v2 [hep-th] 3 Feb 2020 in particular, topology of 4-manifolds and vertex operator algebra. While various connections between these two subjects emerged during the past 2-3 decades, the questions of prime interest in topology | that involve (cutting and gluing) surgery operations | remain, surprisingly, untouched. Similarly, from the algebra perspec- tive, many traditional connections to topology rely on algebraic structures used as an input, i.g. Frobenius algebras in the construction of 2d TQFTs or modular tensor categories in the construction of 3d TQFTs. More recent developments, however, suggest that such algebraic structures can themselves be topological invariants of manifolds, so that one can speak of VOA[M4] or MTC[M3]. Pointing a flashlight directly at these underappreciated aspects can potentially be very beneficial for the development of both subjects. Specifically, we describe a large class of vertex operator algebras (VOAs), each labeled by a choice of a 1 2 BORIS FEIGIN AND SERGEI GUKOV 1 smooth 4-manifold M4 and a root system g of ADE Cartan type. -
Naming Infinity: a True Story of Religious Mysticism And
Naming Infinity Naming Infinity A True Story of Religious Mysticism and Mathematical Creativity Loren Graham and Jean-Michel Kantor The Belknap Press of Harvard University Press Cambridge, Massachusetts London, En gland 2009 Copyright © 2009 by the President and Fellows of Harvard College All rights reserved Printed in the United States of America Library of Congress Cataloging-in-Publication Data Graham, Loren R. Naming infinity : a true story of religious mysticism and mathematical creativity / Loren Graham and Jean-Michel Kantor. â p. cm. Includes bibliographical references and index. ISBN 978-0-674-03293-4 (alk. paper) 1. Mathematics—Russia (Federation)—Religious aspects. 2. Mysticism—Russia (Federation) 3. Mathematics—Russia (Federation)—Philosophy. 4. Mathematics—France—Religious aspects. 5. Mathematics—France—Philosophy. 6. Set theory. I. Kantor, Jean-Michel. II. Title. QA27.R8G73 2009 510.947′0904—dc22â 2008041334 CONTENTS Introduction 1 1. Storming a Monastery 7 2. A Crisis in Mathematics 19 3. The French Trio: Borel, Lebesgue, Baire 33 4. The Russian Trio: Egorov, Luzin, Florensky 66 5. Russian Mathematics and Mysticism 91 6. The Legendary Lusitania 101 7. Fates of the Russian Trio 125 8. Lusitania and After 162 9. The Human in Mathematics, Then and Now 188 Appendix: Luzin’s Personal Archives 205 Notes 212 Acknowledgments 228 Index 231 ILLUSTRATIONS Framed photos of Dmitri Egorov and Pavel Florensky. Photographed by Loren Graham in the basement of the Church of St. Tatiana the Martyr, 2004. 4 Monastery of St. Pantaleimon, Mt. Athos, Greece. 8 Larger and larger circles with segment approaching straight line, as suggested by Nicholas of Cusa. 25 Cantor ternary set. -
L-Invariants of Low Symmetric Powers of Modular Forms and Hida Deformations
L-invariants of low symmetric powers of modular forms and Hida deformations Robert William Harron A Dissertation Presented to the Faculty of Princeton University in Candidacy for the Degree of Doctor of Philosophy Recommended for Acceptance by the Department of Mathematics Adviser: Andrew Wiles September 2009 c Copyright by Robert William Harron, 2009. All Rights Reserved Abstract We obtain formulae for Greenberg's L-invariant of symmetric square and symmetric sixth power motives attached to p-ordinary modular forms in the vein of theorem 3.18 of [GS93]. For the symmetric square of f, the formula obtained relates the L- invariant to the derivative of the p-adic analytic function interpolating the pth Fourier coefficient (equivalently, the unit root of Frobenius) in the Hida family attached to f. We present a different proof than Hida's, [Hi04], with slightly different assumptions. The symmetric sixth power of f requires a bigger p-adic family. We take advantage of a result of Ramakrishnan{Shahidi ([RS07]) on the symmetric cube lifting to GSp(4)=Q, Hida families on the latter ([TU99] and [Hi02]), as well as results of several authors on the Galois representations attached to automorphic representations of GSp(4)=Q, to compute the L-invariant of the symmetric sixth power of f in terms of the derivatives of the p-adic analytic functions interpolating the eigenvalues of Frobenius in a Hida family on GSp(4)=Q. We must however impose stricter conditions on f in this case. Here, Hida's work (e.g. [Hi07]) does not provide answers as specific as ours. -
IMS Bulletin 39(5)
Volume 39 • Issue 5 IMS1935–2010 Bulletin June 2010 IMS Carver Award: Julia Norton Contents Julia A. Norton, Professor Emerita in the 1 IMS Carver Award Department of Statistics and Biostatistics at California State University, East Bay in 2–3 Members’ News: new US National Academy mem- Hayward, California, USA has received bers; Donald Gaver; Marie the 2010 Carver Medal from the Institute Davidian; tributes to Kiyosi of Mathematical Statistics. The presenta- Itô, Ehsanes Saleh tion of the medal will take place August 4 Laha Award recipients 10, 2010 at a special ceremony during the IMS Annual Meeting in Gothenburg, 5 Statistics museum Sweden. Rietz lecture: Michael Stein 6 Professor Norton receivesThe candidate the award for IMS President-Elect is Medallion Preview: Marek for contributions to the IMS throughout 7 Ruth Williams Biskup her career, and especially for her conscien- tious and pivotal service as IMS Treasurer 8 NISS/SAMSI award; during the period when the IMS Business Samuel Kotz Julia A. Norton Office was moved from California to 9 Obituary: Hirotugu Akaike Ohio. 10 Annual survey She said she was greatly surprised to receive the award, commenting, “I just said yes to all sorts of new ideas that came the way of the Institute during my two terms 11 Rick’s Ramblings: with Larry Shepp as Treasurer.” She added, “Like most things, the best part of the job is the fantastic teamwork displayed by the staff. I am most proud of my hand in helping to hire and Terence’s Stuff: Changes, 12 keep [Executive Director] Elyse in our employ.” courses and committees The Carver Medal was created by the IMS in 2002 13 IMS meetings in honor of Harry C. -
President's Report
Volume 38, Number 4 NEWSLETTER July–August 2008 President’s Report Dear Colleagues: I am delighted to announce that our new executive director is Maeve Lewis McCarthy. I am very excited about what AWM will be able to accomplish now that she is in place. (For more about Maeve, see the press release on page 7.) Welcome, Maeve! Thanks are due to the search committee for its thought and energy. These were definitely required because we had some fabulous candidates. Thanks also to Murray State University, Professor McCarthy’s home institution, for its coopera- tion as we worked out the details of her employment with AWM. The AWM Executive Committee has voted to give honorary lifetime mem- IN THIS ISSUE berships to our founding presidents, Mary Gray and Alice T. Schafer. In my role as president, I am continually discovering just how extraordinary AWM is 7 McCarthy Named as an organization. Looking back at its early history, I find it hard to imagine AWM Executive Director how AWM could have come into existence without the vision, work, and persist- ence of these two women. 10 AWM Essay Contest Among newly elected members of the National Academy of Sciences in the physical and mathematical sciences are: 12 AWM Teacher Partnerships 16 MIT woMen In maTH Emily Ann Carter Department of Mechanical and Aerospace Engineering and the Program in 19 Girls’ Angle Applied and Computational Mathematics, Princeton University Lisa Randal Professor of theoretical physics, Department of Physics, Harvard University Elizabeth Thompson Department of Statistics, University of Washington, Seattle A W M The American Academy of Arts and Sciences has also announced its new members. -
Prix Coxeter-James 2007 Coxeter-James Prize
Prix Coxeter-James 2007 Coxeter-James Prize The Coxeter-James Prize was inaugurated to recognize young mathematicians who have made outstanding contributions to mathematical research. The first award was presented in 1978. The Coxeter-James Prize recognizes young mathematicians who have made outstanding contributions to mathematical research. Le prix Coxeter-James rend hommage aux jeunes mathématiciens qui se sont distingués par l’excellence de leur contribution à la recherche mathématique. Il a été décerné pour la première fois en 1978. Le prix Coxeter-James rend hommage aux jeunes mathématiciens qui se sont distingués par l’excellence de leur contribution à la recherche mathématique. Dr. Vinayak Vatsal has made fundamental contributions Vinayak Vatsal a fait d’importantes contributions à la to the Iwasawa Theory of elliptic curves, introducing théorie d’Iwasawa des courbes elliptiques, en y introduisant profound techniques from ergodic theory into the subject des techniques dérivées de la théorie ergodique, et en Dr. Vinayak Vatsal and obtaining startling theorems on the non-vanishing of obtenant des théorèmes impressionnants sur les non- University of British Columbia p-adic L-functions and mu-invariants that had previously annulation de fonctions L p-adiques et de mu-invariants been unobtainable by more orthodox analytic methods. qu’il avait été impossible d’obtenir à l’aide de méthodes RECIPIENTS His 2002 Inventiones paper on the uniform distribution plus orthodoxes. Son article de 2002 intitulé Inventiones LAURÉATS of Heegner points led to the complete solution of a sur la distribution uniforme des points Heegner a abouti fundamental conjecture of Mazur concerning such L- à la solution complète d’une conjecture fondamentale 2006 Jim Geelen functions (now the Vatsal-Cornut theorem). -
American Mathematical Society COUNCIL MINUTES
American Mathematical Society COUNCIL MINUTES New Orleans, Louisiana 05 January 2011 at 1:30 p.m. Prepared January 20, 2011 Abstract The Council of the Society met at 1:30 p.m. on Wednesday, 05 January 2011, in the Mardi Gras E room of the New Orleans Marriott Hotel, 555 Canal Street, New Orleans, LA 70130. These are the minutes of the meeting. Although several items were treated in Executive Session, all actions taken are reported in these minutes. Council Agenda 05 January 2011 Page 2 of 16 Contents I. AGENDA 1. Call to Order 1.1. Opening of the Meeting and Introductions . 4 1.2. 2010 Council Elections........................................4 1.3. Retiring Members. ...........................................4 1.4. Council Members.............................................4 2. Minutes. .........................................................5 2.1. Minutes of the April 2010 Council. 5 2.2. The 05/2010 and 11/2010 Executive Committee and Board of Trustees (ECBT) Meetings.............................................5 3. Consent Agenda....................................................5 3.1. Mathfest Joint Program Committee.. 5 4. Reports of Boards and Standing Committees . 5 4.1. Tellers’ Report on the 2010 Elections [Executive Session]. 5 4.1.1. Tellers’ Report on the Elections of Officers. 5 4.1.2. Tellers’ Report on Elections to the Nominating Committee. 6 4.1.3. Tellers’ Report on Elections to the Editorial Boards Committee. 6 4.2. Executive Committee/Board of Trustees (ECBT). 6 4.2.1. Associate Secretary for the Central Section [Executive Session]. 6 4.2.2. Associate Secretary for the Western Section [Executive Session]. 6 4.2.3. Associate Treasurer [Executive Session] . 7 4.2.4. Dues Levels for the 2012 Membership Year. -
Alexey Zykin Professor at the University of French Polynesia
Alexey Zykin Professor at the University of French Polynesia Personal Details Date and place of birth: 13.06.1984, Moscow, Russia Nationality: Russian Marital status: Single Addresses Address in Polynesia: University of French Polynesia BP 6570, 98702 FAA'A Tahiti, French Polynesia Address in Russia: Independent University of Moscow 11, Bolshoy Vlasyevskiy st., 119002, Moscow, Russia Phone numbers: +689 89 29 11 11 +7 917 591 34 24 E-mail: [email protected] Home page: http://www.mccme.ru/poncelet/pers/zykin.html Languages Russian: Mother tongue English: Fluent French: Fluent Research Interests • Zeta-functions and L-functions (modularity, special values, behaviour in families, Brauer{ Siegel type results, distribution of zeroes). • Algebraic geometry over finite fields (points on curves and varieties over finite fields, zeta-functions). • Families of fields and varieties, asymptotic theory (infinite number fields and function fields, limit zeta-functions). • Abelian varieties and Elliptic Curves (jacobians among abelian varieties, families of abelian varieties over global fields). • Applications of number theory and algebraic geometry to information theory (cryptog- raphy, error-correcting codes, sphere packings). Publications Publications in peer-reviewed journals: • On logarithmic derivatives of zeta functions in families of global fields (with P. Lebacque), International Journal of Number Theory, Vol. 7 (2011), Num. 8, 2139{2156. • Asymptotic methods in number theory and algebraic geometry (with P. Lebacque), Pub- lications Math´ematiquesde Besan¸con,2011, 47{73. • Asymptotic properties of Dedekind zeta functions in families of number fields, Journal de Th´eoriedes Nombres de Bordeaux, 22 (2010), Num. 3, 689{696. 1 • Jacobians among abelian threefolds: a formula of Klein and a question of Serre (with G.