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Of the American Mathematical Society August 2017 Volume 64, Number 7
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society August 2017 Volume 64, Number 7 The Mathematics of Gravitational Waves: A Two-Part Feature page 684 The Travel Ban: Affected Mathematicians Tell Their Stories page 678 The Global Math Project: Uplifting Mathematics for All page 712 2015–2016 Doctoral Degrees Conferred page 727 Gravitational waves are produced by black holes spiraling inward (see page 674). American Mathematical Society LEARNING ® MEDIA MATHSCINET ONLINE RESOURCES MATHEMATICS WASHINGTON, DC CONFERENCES MATHEMATICAL INCLUSION REVIEWS STUDENTS MENTORING PROFESSION GRAD PUBLISHING STUDENTS OUTREACH TOOLS EMPLOYMENT MATH VISUALIZATIONS EXCLUSION TEACHING CAREERS MATH STEM ART REVIEWS MEETINGS FUNDING WORKSHOPS BOOKS EDUCATION MATH ADVOCACY NETWORKING DIVERSITY blogs.ams.org Notices of the American Mathematical Society August 2017 FEATURED 684684 718 26 678 Gravitational Waves The Graduate Student The Travel Ban: Affected Introduction Section Mathematicians Tell Their by Christina Sormani Karen E. Smith Interview Stories How the Green Light was Given for by Laure Flapan Gravitational Wave Research by Alexander Diaz-Lopez, Allyn by C. Denson Hill and Paweł Nurowski WHAT IS...a CR Submanifold? Jackson, and Stephen Kennedy by Phillip S. Harrington and Andrew Gravitational Waves and Their Raich Mathematics by Lydia Bieri, David Garfinkle, and Nicolás Yunes This season of the Perseid meteor shower August 12 and the third sighting in June make our cover feature on the discovery of gravitational waves -
Hilbert Constance Reid
Hilbert Constance Reid Hilbert c COPERNICUS AN IMPRINT OF SPRINGER-VERLAG © 1996 Springer Science+Business Media New York Originally published by Springer-Verlag New York, Inc in 1996 All rights reserved. No part ofthis publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Library ofCongress Cataloging·in-Publication Data Reid, Constance. Hilbert/Constance Reid. p. Ctn. Originally published: Berlin; New York: Springer-Verlag, 1970. Includes bibliographical references and index. ISBN 978-0-387-94674-0 ISBN 978-1-4612-0739-9 (eBook) DOI 10.1007/978-1-4612-0739-9 I. Hilbert, David, 1862-1943. 2. Mathematicians-Germany Biography. 1. Title. QA29.HsR4 1996 SIO'.92-dc20 [B] 96-33753 Manufactured in the United States of America. Printed on acid-free paper. 9 8 7 6 543 2 1 ISBN 978-0-387-94674-0 SPIN 10524543 Questions upon Rereading Hilbert By 1965 I had written several popular books, such as From liro to Infinity and A Long Way from Euclid, in which I had attempted to explain certain easily grasped, although often quite sophisticated, mathematical ideas for readers very much like myself-interested in mathematics but essentially untrained. At this point, with almost no mathematical training and never having done any bio graphical writing, I became determined to write the life of David Hilbert, whom many considered the profoundest mathematician of the early part of the 20th century. Now, thirty years later, rereading Hilbert, certain questions come to my mind. -
Investigating Statistical Privacy Frameworks from the Perspective of Hypothesis Testing 234 Able Quantity
Investigating Statistical Privacy Frameworks from the Perspective of Hypothesis Testing 234 able quantity. Only a limited number of previous works which can provide a natural and interpretable guide- [29, 34, 35] have investigated the question of how to line for selecting proper privacy parameters by system select a proper value of ǫ, but these approaches ei- designers and researchers. Furthermore, we extend our ther require complicated economic models or lack the analysis on unbounded DP to bounded DP and the ap- analysis of adversaries with arbitrary auxiliary informa- proximate (ǫ, δ)-DP. tion (see Section 2.3 for more details). Our work is in- Impact of Auxiliary Information. The conjecture spired by the interpretation of differential privacy via that auxiliary information can influence the design of hypothesis testing, initially introduced by Wasserman DP mechanisms has been made in prior work [8, 28, 32, and Zhou [27, 30, 60]. However, this interpretation has 33, 39, 65]. We therefore investigate the adversary’s ca- not been systematically investigated before in the con- pability based on hypothesis testing under three types text of our research objective, i.e., reasoning about the of auxiliary information: the prior distribution of the in- choice of the privacy parameter ǫ (see Section 2.4 for put record, the correlation across records, and the corre- more details). lation across time. Our analysis demonstrates that the We consider hypothesis testing [2, 45, 61] as the tool auxiliary information indeed influences the appropriate used by the adversary to infer sensitive information of selection of ǫ. The results suggest that, when possible an individual record (e.g., the presence or absence of and available, the practitioners of DP should explicitly a record in the database for unbounded DP) from the incorporate adversary’s auxiliary information into the outputs of privacy mechanisms. -
The Singular Structure and Regularity of Stationary Varifolds 3
THE SINGULAR STRUCTURE AND REGULARITY OF STATIONARY VARIFOLDS AARON NABER AND DANIELE VALTORTA ABSTRACT. If one considers an integral varifold Im M with bounded mean curvature, and if S k(I) x ⊆ ≡ { ∈ M : no tangent cone at x is k + 1-symmetric is the standard stratification of the singular set, then it is well } known that dim S k k. In complete generality nothing else is known about the singular sets S k(I). In this ≤ paper we prove for a general integral varifold with bounded mean curvature, in particular a stationary varifold, that every stratum S k(I) is k-rectifiable. In fact, we prove for k-a.e. point x S k that there exists a unique ∈ k-plane Vk such that every tangent cone at x is of the form V C for some cone C. n 1 n × In the case of minimizing hypersurfaces I − M we can go further. Indeed, we can show that the singular ⊆ set S (I), which is known to satisfy dim S (I) n 8, is in fact n 8 rectifiable with uniformly finite n 8 measure. ≤ − − − 7 An effective version of this allows us to prove that the second fundamental form A has apriori estimates in Lweak on I, an estimate which is sharp as A is not in L7 for the Simons cone. In fact, we prove the much stronger | | 7 estimate that the regularity scale rI has Lweak-estimates. The above results are in fact just applications of a new class of estimates we prove on the quantitative k k k k + stratifications S ǫ,r and S ǫ S ǫ,0. -
Geometric Measure Theory and Differential Inclusions
GEOMETRIC MEASURE THEORY AND DIFFERENTIAL INCLUSIONS C. DE LELLIS, G. DE PHILIPPIS, B. KIRCHHEIM, AND R. TIONE Abstract. In this paper we consider Lipschitz graphs of functions which are stationary points of strictly polyconvex energies. Such graphs can be thought as integral currents, resp. varifolds, which are stationary for some elliptic integrands. The regularity theory for the latter is a widely open problem, in particular no counterpart of the classical Allard’s theorem is known. We address the issue from the point of view of differential inclusions and we show that the relevant ones do not contain the class of laminates which are used in [22] and [25] to construct nonregular solutions. Our result is thus an indication that an Allard’s type result might be valid for general elliptic integrands. We conclude the paper by listing a series of open questions concerning the regularity of stationary points for elliptic integrands. 1. Introduction m 1 n×m Let Ω ⊂ R be open and f 2 C (R ; R) be a (strictly) polyconvex function, i.e. such that there is a (strictly) convex g 2 C1 such that f(X) = g(Φ(X)), where Φ(X) denotes the vector of n subdeterminants of X of all orders. We then consider the following energy E : Lip(Ω; R ) ! R: E(u) := f(Du)dx : (1) ˆΩ n Definition 1.1. Consider a map u¯ 2 Lip(Ω; R ). The one-parameter family of functions u¯ + "v will be called outer variations and u¯ will be called critical for E if d E 1 n (¯u + "v) = 0 8v 2 Cc (Ω; R ) : d" "=0 1 m 1 Given a vector field Φ 2 Cc (Ω; R ) we let X" be its flow . -
2008 Annual Report
2008 Annual Report NATIONAL ACADEMY OF ENGINEERING ENGINEERING THE FUTURE 1 Letter from the President 3 In Service to the Nation 3 Mission Statement 4 Program Reports 4 Engineering Education 4 Center for the Advancement of Scholarship on Engineering Education 6 Technological Literacy 6 Public Understanding of Engineering Developing Effective Messages Media Relations Public Relations Grand Challenges for Engineering 8 Center for Engineering, Ethics, and Society 9 Diversity in the Engineering Workforce Engineer Girl! Website Engineer Your Life Project Engineering Equity Extension Service 10 Frontiers of Engineering Armstrong Endowment for Young Engineers-Gilbreth Lectures 12 Engineering and Health Care 14 Technology and Peace Building 14 Technology for a Quieter America 15 America’s Energy Future 16 Terrorism and the Electric Power-Delivery System 16 U.S.-China Cooperation on Electricity from Renewables 17 U.S.-China Symposium on Science and Technology Strategic Policy 17 Offshoring of Engineering 18 Gathering Storm Still Frames the Policy Debate 20 2008 NAE Awards Recipients 22 2008 New Members and Foreign Associates 24 2008 NAE Anniversary Members 28 2008 Private Contributions 28 Einstein Society 28 Heritage Society 29 Golden Bridge Society 29 Catalyst Society 30 Rosette Society 30 Challenge Society 30 Charter Society 31 Other Individual Donors 34 The Presidents’ Circle 34 Corporations, Foundations, and Other Organizations 35 National Academy of Engineering Fund Financial Report 37 Report of Independent Certified Public Accountants 41 Notes to Financial Statements 53 Officers 53 Councillors 54 Staff 54 NAE Publications Letter from the President Engineering is critical to meeting the fundamental challenges facing the U.S. economy in the 21st century. -
MA3403 Algebraic Topology Lecturer: Gereon Quick Lecture 21
MA3403 Algebraic Topology Lecturer: Gereon Quick Lecture 21 21. Applications of cup products in cohomology We are going to see some examples where we calculate or apply multiplicative structures on cohomology. But we start with a couple of facts we forgot to mention last time. Relative cup products Let (X;A) be a pair of spaces. The formula which specifies the cup product by its effect on a simplex (' [ )(σ) = '(σj[e0;:::;ep]) (σj[ep;:::;ep+q]) extends to relative cohomology. For, if σ : ∆p+q ! X has image in A, then so does any restriction of σ. Thus, if either ' or vanishes on chains with image in A, then so does ' [ . Hence we get relative cup product maps Hp(X; R) × Hq(X;A; R) ! Hp+q(X;A; R) Hp(X;A; R) × Hq(X; R) ! Hp+q(X;A; R) Hp(X;A; R) × Hq(X;A; R) ! Hp+q(X;A; R): More generally, assume we have two open subsets A and B of X. Then the formula for ' [ on cochains implies that cup product yields a map Sp(X;A; R) × Sq(X;B; R) ! Sp+q(X;A + B; R) where Sn(X;A+B; R) denotes the subgroup of Sn(X; R) of cochains which vanish on sums of chains in A and chains in B. The natural inclusion Sn(X;A [ B; R) ,! Sn(X;A + B; R) induces an isomorphism in cohomology. For we have a map of long exact coho- mology sequences Hn(A [ B) / Hn(X) / Hn(X;A [ B) / Hn+1(A [ B) / Hn+1(X) Hn(A + B) / Hn(X) / Hn(X;A + B) / Hn+1(A + B) / Hn+1(X) 1 2 where we omit the coefficients. -
The Book of Abstracts
1st Joint Meeting of the American Mathematical Society and the New Zealand Mathematical Society Victoria University of Wellington Wellington, New Zealand December 12{15, 2007 American Mathematical Society New Zealand Mathematical Society Contents Timetables viii Plenary Addresses . viii Special Sessions ............................. ix Computability Theory . ix Dynamical Systems and Ergodic Theory . x Dynamics and Control of Systems: Theory and Applications to Biomedicine . xi Geometric Numerical Integration . xiii Group Theory, Actions, and Computation . xiv History and Philosophy of Mathematics . xv Hopf Algebras and Quantum Groups . xvi Infinite Dimensional Groups and Their Actions . xvii Integrability of Continuous and Discrete Evolution Systems . xvii Matroids, Graphs, and Complexity . xviii New Trends in Spectral Analysis and PDE . xix Quantum Topology . xx Special Functions and Orthogonal Polynomials . xx University Mathematics Education . xxii Water-Wave Scattering, Focusing on Wave-Ice Interactions . xxiii General Contributions . xxiv Plenary Addresses 1 Marston Conder . 1 Rod Downey . 1 Michael Freedman . 1 Bruce Kleiner . 2 Gaven Martin . 2 Assaf Naor . 3 Theodore A Slaman . 3 Matt Visser . 4 Computability Theory 5 George Barmpalias . 5 Paul Brodhead . 5 Cristian S Calude . 5 Douglas Cenzer . 6 Chi Tat Chong . 6 Barbara F Csima . 6 QiFeng ................................... 6 Johanna Franklin . 7 Noam Greenberg . 7 Denis R Hirschfeldt . 7 Carl G Jockusch Jr . 8 Bakhadyr Khoussainov . 8 Bj¨ornKjos-Hanssen . 8 Antonio Montalban . 9 Ng, Keng Meng . 9 Andre Nies . 9 i Jan Reimann . 10 Ludwig Staiger . 10 Frank Stephan . 10 Hugh Woodin . 11 Guohua Wu . 11 Dynamical Systems and Ergodic Theory 12 Boris Baeumer . 12 Mathias Beiglb¨ock . 12 Arno Berger . 12 Keith Burns . 13 Dmitry Dolgopyat . 13 Anthony Dooley . -
Homological Mirror Symmetry for the Genus 2 Curve in an Abelian Variety and Its Generalized Strominger-Yau-Zaslow Mirror by Cath
Homological mirror symmetry for the genus 2 curve in an abelian variety and its generalized Strominger-Yau-Zaslow mirror by Catherine Kendall Asaro Cannizzo A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Mathematics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Denis Auroux, Chair Professor David Nadler Professor Marjorie Shapiro Spring 2019 Homological mirror symmetry for the genus 2 curve in an abelian variety and its generalized Strominger-Yau-Zaslow mirror Copyright 2019 by Catherine Kendall Asaro Cannizzo 1 Abstract Homological mirror symmetry for the genus 2 curve in an abelian variety and its generalized Strominger-Yau-Zaslow mirror by Catherine Kendall Asaro Cannizzo Doctor of Philosophy in Mathematics University of California, Berkeley Professor Denis Auroux, Chair Motivated by observations in physics, mirror symmetry is the concept that certain mani- folds come in pairs X and Y such that the complex geometry on X mirrors the symplectic geometry on Y . It allows one to deduce information about Y from known properties of X. Strominger-Yau-Zaslow (1996) described how such pairs arise geometrically as torus fibra- tions with the same base and related fibers, known as SYZ mirror symmetry. Kontsevich (1994) conjectured that a complex invariant on X (the bounded derived category of coherent sheaves) should be equivalent to a symplectic invariant of Y (the Fukaya category). This is known as homological mirror symmetry. In this project, we first use the construction of SYZ mirrors for hypersurfaces in abelian varieties following Abouzaid-Auroux-Katzarkov, in order to obtain X and Y as manifolds. -
2009 SIAM Annual Meeting Is Being Held Rooms Sell out Quickly!) in Conjunction with the Community Lecture Wednesday, July 8, 6:15 – 7:15 PM I.E
Join SIAM in Denverwww.siam.org/meetings/an09 Organizing Committee Mihai Anitescu, Argonne National Laboratory Andrew Conn, IBM T. J. Watson Research Center Lenore Cowen, Tufts University William McEneaney, University of California, San Diego Esmond Ng, Lawrence Berkeley National Laboratory Donald Estep, Colorado State University Lori Freitag-Diachin (co-chair), Lawrence Livermore National Laboratory Padma Raghavan, Pennsylvania State University Jonathan Rubin, University of Pittsburgh Invited Presentations Björn Sandstede, University of Surrey, United Plenary Speakers Kingdom Heinz-Otto Kreiss, KTH Stockholm, Sweden Rob Schreiber, Hewlett Packard Karl Kunisch*, University of Graz, Austria Tao Tang, Hong Kong Baptist University, Hong Kong Ulisses Mello, IBM Research Andy Wathen (co-chair), University of Oxford, * Joint speaker with the 2009 SIAM Conference on United Kingdom Control and Its Applications Thaleia Zariphopoulou, University of Texas, Austin Topical Speakers Alberto Bressan, Pennsylvania State University Prizes and Awards Luncheon Russel E. Caflisch, University of California, Los Angeles The following prizes and awards will be presented Stephen Coombes, University of Nottingham, at the prizes and awards luncheon on Tuesday, United Kingdom July 7, 12:30 – 2:00 PM. Michael C. Ferris, University of Wisconsin Wen-mei Hwu, University of Illinois at Urbana-Champaign I. E. Block Community Lecture Ioannis Karatzas, Columbia University Theodore von Kármán Prize Lecture Charles E. Leiserson, Cilk Arts and Massachusetts AWM-SIAM Sonia Kovalevsky Lecture Institute of Technology W. T. and Idalia Reid Prize in Mathematics Lecture Lois Curfman McInnes, Argonne National Laboratory The John von Neumann Lecture Denver images courtesy Bruce Younggreen, and Denver Visitors and Convention Bureau and Denver Visitors Younggreen, Denver images courtesy Bruce Juan C. -
Digital Communication Systems 2.2 Optimal Source Coding
Digital Communication Systems EES 452 Asst. Prof. Dr. Prapun Suksompong [email protected] 2. Source Coding 2.2 Optimal Source Coding: Huffman Coding: Origin, Recipe, MATLAB Implementation 1 Examples of Prefix Codes Nonsingular Fixed-Length Code Shannon–Fano code Huffman Code 2 Prof. Robert Fano (1917-2016) Shannon Award (1976 ) Shannon–Fano Code Proposed in Shannon’s “A Mathematical Theory of Communication” in 1948 The method was attributed to Fano, who later published it as a technical report. Fano, R.M. (1949). “The transmission of information”. Technical Report No. 65. Cambridge (Mass.), USA: Research Laboratory of Electronics at MIT. Should not be confused with Shannon coding, the coding method used to prove Shannon's noiseless coding theorem, or with Shannon–Fano–Elias coding (also known as Elias coding), the precursor to arithmetic coding. 3 Claude E. Shannon Award Claude E. Shannon (1972) Elwyn R. Berlekamp (1993) Sergio Verdu (2007) David S. Slepian (1974) Aaron D. Wyner (1994) Robert M. Gray (2008) Robert M. Fano (1976) G. David Forney, Jr. (1995) Jorma Rissanen (2009) Peter Elias (1977) Imre Csiszár (1996) Te Sun Han (2010) Mark S. Pinsker (1978) Jacob Ziv (1997) Shlomo Shamai (Shitz) (2011) Jacob Wolfowitz (1979) Neil J. A. Sloane (1998) Abbas El Gamal (2012) W. Wesley Peterson (1981) Tadao Kasami (1999) Katalin Marton (2013) Irving S. Reed (1982) Thomas Kailath (2000) János Körner (2014) Robert G. Gallager (1983) Jack KeilWolf (2001) Arthur Robert Calderbank (2015) Solomon W. Golomb (1985) Toby Berger (2002) Alexander S. Holevo (2016) William L. Root (1986) Lloyd R. Welch (2003) David Tse (2017) James L. -
Early History of the Riemann Hypothesis in Positive Characteristic
The Legacy of Bernhard Riemann c Higher Education Press After One Hundred and Fifty Years and International Press ALM 35, pp. 595–631 Beijing–Boston Early History of the Riemann Hypothesis in Positive Characteristic Frans Oort∗ , Norbert Schappacher† Abstract The classical Riemann Hypothesis RH is among the most prominent unsolved prob- lems in modern mathematics. The development of Number Theory in the 19th century spawned an arithmetic theory of polynomials over finite fields in which an analogue of the Riemann Hypothesis suggested itself. We describe the history of this topic essentially between 1920 and 1940. This includes the proof of the ana- logue of the Riemann Hyothesis for elliptic curves over a finite field, and various ideas about how to generalize this to curves of higher genus. The 1930ies were also a period of conflicting views about the right method to approach this problem. The later history, from the proof by Weil of the Riemann Hypothesis in charac- teristic p for all algebraic curves over a finite field, to the Weil conjectures, proofs by Grothendieck, Deligne and many others, as well as developments up to now are described in the second part of this diptych: [44]. 2000 Mathematics Subject Classification: 14G15, 11M99, 14H52. Keywords and Phrases: Riemann Hypothesis, rational points over a finite field. Contents 1 From Richard Dedekind to Emil Artin 597 2 Some formulas for zeta functions. The Riemann Hypothesis in characteristic p 600 3 F.K. Schmidt 603 ∗Department of Mathematics, Utrecht University, Princetonplein 5, 3584 CC