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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 -
Contemporary Mathematics 220
CONTEMPORARY MATHEMATICS 220 Homotopy Theory via Algebraic Geometry and Group Representations Proceedings of a Conference on Homotopy Theory March 23-27, 1997 Northwestern University Mark Mahowald Stewart Priddy Editors http://dx.doi.org/10.1090/conm/220 Selected Titles in This Series 220 Mark Mahowald and Stewart Priddy, Editors, Homotopy theory via algebraic geometry and group representations, 1998 219 Marc Henneaux, Joseph Krasil'shchik, and Alexandre Vinogradov, Editors, Secondary calculus and cohomological physics, 1998 218 Jan Mandel, Charbel Farhat, and Xiao-Chuan Cai, Editors, Domain decomposition methods 10, 1998 217 Eric Carlen, Evans M. Harrell, and Michael Loss, Editors, Advances in differential equations and mathematical physics, 1998 216 Akram Aldroubi and EnBing Lin, Editors, Wavelets, multiwavelets, and their applications, 1998 215 M. G. Nerurkar, D.P. Dokken, and D. B. Ellis, Editors, Topological dynamics and applications, 1998 214 Lewis A. Coburn and Marc A. Rieffel, Editors, Perspectives on quantization, 1998 213 Farhad Jafari, Barbara D. MacCluer, Carl C. Cowen, and A. Duane Porter, Editors, Studies on composition operators, 1998 212 E. Ramirez de Arellano, N. Salinas, M. V. Shapiro, and N. L. Vasilevski, Editors, Operator theory for complex and hypercomplex analysis, 1998 211 J6zef Dodziuk and Linda Keen, Editors, Lipa's legacy: Proceedings from the Bers Colloquium, 1997 210 V. Kumar Murty and Michel Waldschmidt, Editors, Number theory, 1998 209 Steven Cox and Irena Lasiecka, Editors, Optimization methods in partial differential equations, 1997 208 MichelL. Lapidus, Lawrence H. Harper, and Adolfo J. Rumbos, Editors, Harmonic analysis and nonlinear differential equations: A volume in honor of Victor L. Shapiro, 1997 207 Yujiro Kawamata and Vyacheslav V. -
Mathematics People, Volume 51, Number 6
Mathematics People 2004–2005 AMS Centennial Fellowships Awarded The AMS has awarded two Centennial Fellowships for 2004–2005. The recipients are JINHO BAIK of the University of Michigan and NITU KITCHLOO of Johns Hopkins Univer- sity. The amount of each fellowship is $60,000. The Cen- tennial Fellows also receive an expense allowance of $1,700 and a complimentary Society membership for one year. Jinho Baik Jinho Baik received his Ph.D. in 1999 from the Courant Institute of Mathematical Sciences, New York University, under the direction of Percy Deift. He was a Veblen Jinho Baik Nitu Kitchloo Instructor at Princeton University and the Institute for Advanced Study during 1999–2002, and an assistant pro- loop groups, and Kac-Moody groups. His current interests fessor at Princeton University during 2002–2003. Since involve studying the topology of symplectomorphism 2002 he has been an assistant professor at the University groups. He is also working on the topology of certain in- of Michigan. finite loop spaces arising from spectra related to complex Baik has been applying methods from integrable sys- cobordism. tems to probability, combinatorics, and statistical physics. Please note: Information about the competition for the In particular, asymptotic problems on random matrices, 2005–2006 AMS Centennial Fellowships will be published random permutations and orthogonal polynomials, and in the “Mathematics Opportunities” section of an upcom- their interrelations have been his main research interest. ing issue of the Notices. He plans to use the fellowship to visit the Courant In- stitute of Mathematical Sciences. —Allyn Jackson Nitu Kitchloo Nitu Kitchloo received his Ph.D. -
Lecture Notes in Mathematics
Lecture Notes in Mathematics For information about Vols. 1-1145 please contact your bookseller Vol. 1173: H. DeHs, M. Knebusch, Locally Semialgebraic Spaces. XVI, or Springer-Verlag. 329 pages. 1g95, Vol. 1146: 5eminaire d'Aigebre Paul Dubreil et Marie-Paula Malliavin. Vol. 1174: Categories in Continuum Physics, Buffalo 1982. Seminar. Proceedings, 1g63-1984. Edite par M.-P. Malliavin. IV, 420 pages. Edited by F.W. Lawvere and S.H. Schanuel. V, t26 pages. t986. 1985. Vol. 1175: K. Mathiak, Valuations of Skew Fields and Projective Vol. 1147: M. Wschebor, Surfaces Aleatoires. VII, 11t pages. 1985. Hjelmslev Spaces. VII, 116 pages. 1986. Vol. 1t48: Mark A. Kon, Probability Distributions in Quantum Statistical Vol. 1176: R.R. Bruner, J.P. May, J.E. McClure, M. Steinberger, Mechanics. V, 12t pages. 1985. Hoo Ring Spectra and their Applications. VII, 388 pages. 1988. Vol. 1149: Universal Algebra and Lattice Theory. Proceedings, 1984. Vol. 1t77: Representation Theory I. Finite Dimensional Algebras. Edited by S. D. Comer. VI, 282 pages. 1985. Proceedings, t984. Edited by V. Dlab, P. Gabriel and G. Michler. XV, 340 pages. 1g86. Vol. 1150: B. Kawohl, Rearrangements and Convexity of Level Sets in Vol. 1178: Representation Theory II. Groups and Orders. Proceed PDE. V, 136 pages. 1985. ings, 1984. Edited by V. Dlab, P. Gabriel and G. Michler. XV, 370 Vol 1151: Ordinary and Partial Differential Equations. Proceedings, pages. 1986. 1984. Edited by B.D. Sleeman and R.J. Jarvis. XIV, 357 pages. 1985. Vol. 1179: Shi J .-Y. The Kazhdan-Lusztig Cells in Certain Affine Weyl Vol. 1152: H. Widom, Asymptotic Expansions for Pseudodifferential Groups. -
In the Supreme Court of Pennsylvania League Of
Received 2/15/2018 11:52:50 PM Supreme Court Middle District Filed 2/15/2018 11:52:00 PM Supreme Court Middle District 159 MM 2017 IN THE SUPREME COURT OF PENNSYLVANIA LEAGUE OF WOMEN VOTERS OF : PENNSYLVANIA, et al., : : Petitioners, : v. : Docket No. 159 MM 2017 : THE COMMONWEALTH OF : PENNSYLVANIA, et al., : : Respondents. : STATEMENT OF RESPONDENT THOMAS W. WOLF IN SUPPORT OF HIS PROPOSED REMEDIAL CONGRESSIONAL MAP PURSUANT TO COURT’S ORDERS OF JANUARY 22 AND JANUARY 26, 2018 TABLE OF CONTENTS I. The Governor’s Proposed Map Is Fair, Constitutional, and Respects the Criteria Set Forth by the Court. ............................................ 4 A. The Governor’s Map Respects Traditional Districting Principles ............................................................................................... 4 B. Statistical Analysis Underscores the Key Attributes of the Governor’s Map .................................................................................. 12 1. Splits of Political Subdivisions ................................................. 12 2. Compactness Scores .................................................................. 12 C. Mathematical Analysis Demonstrates That the Governor’s Map, in Contrast to Legislative Respondents’ Map, Gives Pennsylvania Voters a Fair and Unbiased Opportunity to Participate in Congressional Elections. ............................................... 13 II. This Court Has the Authority – and, Indeed, the Responsibility -- to Adopt a Remedial Map. ......................................................................... -
A Computational Approach to Measuring Vote Elasticity and Competitiveness
A Computational Approach to Measuring Vote Elasticity and Competitiveness Daryl DeFord∗ CSAIL, Massachusetts Institute of Technology Moon Duchin Department of Mathematics, Tufts University Justin Solomon CSAIL, Massachusetts Institute of Technology May 27, 2020 Abstract The recent wave of attention to partisan gerrymandering has come with a push to refine or replace the laws that govern political redistricting around the country. A common element in several states' reform efforts has been the inclusion of com- petitiveness metrics, or scores that evaluate a districting plan based on the extent to which district-level outcomes are in play or are likely to be closely contested. In this paper, we examine several classes of competitiveness metrics motivated by recent reform proposals and then evaluate their potential outcomes across large ensembles of districting plans at the Congressional and state Senate levels. This is part of a growing literature using MCMC techniques from applied statistics to situate plans and criteria in the context of valid redistricting alternatives. Our empirical analysis focuses on five states|Utah, Georgia, Wisconsin, Virginia, and Massachusetts|chosen to represent a range of partisan attributes. We highlight arXiv:2005.12731v1 [cs.CY] 26 May 2020 situation-specific difficulties in creating good competitiveness metrics and show that optimizing competitiveness can produce unintended consequences on other partisan metrics. These results demonstrate the importance of (1) avoiding writing detailed metric constraints into long-lasting constitutional reform and (2) carrying out careful mathematical modeling on real geo-electoral data in each redistricting cycle. Keywords: Redistricting, Gerrymandering, Markov Chains, Competitiveness ∗The authors gratefully acknowledge the generous support of the Prof. -
Bienvenue Au Numéro De Septembre 2020Des Notes De La
Bienvenue au numéro de septembre 2020 des Notes de la SMC Table des matières Septembre 2020 : tome 52, no. 4 Article de couverture La maison canadienne des mathématiques — Javad Mashreghi Éditorial Vivre en des temps intéressants — Robert Dawson Comptes rendus Brefs comptes rendus Notes pédagogiques No, We’re Not There Yet: Teaching Mathematics at the Time of COVID-19 and Beyond — Kseniya Garaschuk and Veselin Jungic Notes de la SCHPM Ada Lovelace: New Light on her Mathematics — Adrian Rice Richard Kenneth Guy (1916-2020) Prologue — R. Scheidler and R. Woodrow Richard Guy et la théorie des jeux — R. Nowakowski Richard Guy et la géométrie — T. Bisztriczky Richard Guy et la théorie des nombres — M. J. Jacobson Jr., R. Scheidler and H. C. Williams Richard Guy et le mentorat — R. Scheidler Épilogue Appel de candidatures Prix de recherche de la SMC 2021 Rédacteur ou rédactrice associé.e.s du JCM/BCM 2021 Rédacteur ou rédactrice associé.e.s pour CRUX 2020 Prix Cathleen-Synge-Morawetz 2021 Prix d'excellence en enseignement 2021 Rédacteurs ou rédactrices en chef au JCM 2022 Concours Concours mathématiques de la SMC Réunions de la SMC Résumé de la réunion de la SMC sur la recherche et l'éducation au temps de la COVID-19 — Sarah Watson Réunion virtuelle d'hiver 2020 de la SMC Notices nécrologiques Elmer Melvin Tory (1928-2020) Peter Borwein (1953-2020) — Veselin Jungic Annonces Director for the Pacic Institute for the Mathematical Sciences Équipe éditoriale Équipe éditoriale La maison canadienne des mathématiques Article de couverture Septembre 2020 (tome 52, no. 4) Javad Mashreghi (Université Laval) Président de la SMC Nous devions nous réunir cet été à Ottawa et célébrer le 75e anniversaire de la création de la Société mathématique du Canada. -
On the Non-Existence of Elements of Kervaire Invariant
ON THE NON-EXISTENCE OF ELEMENTS OF KERVAIRE INVARIANT ONE M. A. HILL, M. J. HOPKINS, AND D. C. RAVENEL Dedicated to Mark Mahowald 0 Abstract. We show that the Kervaire invariant one elements θj ∈ π2j+1−2S exist only for j ≤ 6. By Browder’s Theorem, this means that smooth framed manifolds of Kervaire invariant one exist only in dimensions 2, 6, 14, 30, 62, and possibly 126. Except for dimension 126 this resolves a longstanding problem in algebraic topology. Contents 1. Introduction 1 2. Equivariant stable homotopy theory 8 3. Mackey functors, homology and homotopy 35 4. The slice filtration 44 5. The complex cobordism spectrum 63 6. The Slice Theorem and the Reduction Theorem 76 7. The Reduction Theorem 80 8. The Gap Theorem 88 9. The Periodicity Theorem 89 10. The Homotopy Fixed Point Theorem 101 11. The Detection Theorem 103 Appendix A. The category of equivariant orthogonal spectra 118 Appendix B. Homotopy theory of equivariant orthogonal spectra 143 References 217 arXiv:0908.3724v4 [math.AT] 25 May 2015 1. Introduction The existence of smooth framed manifolds of Kervaire invariant one is one of the oldest unresolved issues in differential and algebraic topology. The question originated in the work of Pontryagin in the 1930’s. It took a definitive form in the paper [41] of Kervaire in which he constructed a combinatorial 10-manifold with no smooth structure, and in the work of Kervaire-Milnor [42] on h-cobordism classes M. A. Hill was partially supported by NSF grants DMS-0905160 , DMS-1307896 and the Sloan foundation. -
Fighting for Tenure the Jenny Harrison Case Opens Pandora's
Calendar of AMS Meetings and Conferences This calendar lists all meetings and conferences approved prior to the date this issue insofar as is possible. Instructions for submission of abstracts can be found in the went to press. The summer and annual meetings are joint meetings with the Mathe January 1993 issue of the Notices on page 46. Abstracts of papers to be presented at matical Association of America. the meeting must be received at the headquarters of the Society in Providence, Rhode Abstracts of papers presented at a meeting of the Society are published in the Island, on or before the deadline given below for the meeting. Note that the deadline for journal Abstracts of papers presented to the American Mathematical Society in the abstracts for consideration for presentation at special sessions is usually three weeks issue corresponding to that of the Notices which contains the program of the meeting, earlier than that specified below. Meetings Abstract Program Meeting# Date Place Deadline Issue 890 t March 18-19, 1994 Lexington, Kentucky Expired March 891 t March 25-26, 1994 Manhattan, Kansas Expired March 892 t April8-10, 1994 Brooklyn, New York Expired April 893 t June 16-18, 1994 Eugene, Oregon April4 May-June 894 • August 15-17, 1994 (96th Summer Meeting) Minneapolis, Minnesota May 17 July-August 895 • October 28-29, 1994 Stillwater, Oklahoma August 3 October 896 • November 11-13, 1994 Richmond, Virginia August 3 October 897 • January 4-7, 1995 (101st Annual Meeting) San Francisco, California October 1 December March 4-5, 1995 -
REMEMBERING MARK MAHOWALD 1931–2013 Mark Mahowald Was a Dominant Figure in Algebraic Topology for Decades. After Being Trained
REMEMBERING MARK MAHOWALD 1931–2013 DOUGLAS C. RAVENEL WITH CONTRIBUTIONS BY MARTIN C. TANGORA, STEWART B. PRIDDY, DONALD M. DAVIS, MARK J. BEHRENS AND WEN-HSIUNG LIN UNABRIDGED VERSION OF A SIMILAR ARTICLE THAT APPEARED IN THE JULY 2016 ISSUE OF THE NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, PHOTOS NOT INCLUDED Mark Mahowald was a dominant figure in algebraic topology for decades. After being trained as an analyst he became a self trained homotopy theorist in the early 1960s. His 1967 AMS Memoir The metastable homotopy of S n, with its dozens of charts packed with arcane information, established him as a master of computations related to the homotopy groups of spheres. It came to be known in the field simply as “the red book.” It was the unanimous opinion of experts that he knew this subject far better than anyone else. His insight and intuition were legendary. Countless coworkers benefited from his ideas and advice. He was born on December 1, 1931, in Albany, Minnesota, a very small and mostly German Catholic community. He was one of seven children. His father was a family physician who ran his practice out of his home. There was an enyclopedia in the house which Mark would consult whenever he was curious about something. He was largely self taught. He also spent a lot of time on the nearby farm that his father owned. Among his six siblings, two would become academics, one a medical doctor and one a Jesuit priest. Mark first attended college at Carnegie Tech (now Carnegie Mellon University) in Pitts- burgh and planned to major in chemical engineering. -
Partisan Gerrymandering and the Efficiency
OPINION OPINION Post-Quantum A Formula Goes to Court: Cryptography—A New Partisan Gerrymandering Opportunity and Challenge forand the Efficiency Gap the Mathematics CommunityMira Bernstein and Moon Duchin Note: The opinions expressed here are not necessarily those of Notices. Jintai Ding and Daniel Smith-Tone Responses on the Notices webpage are invited. Note: The opinions expressed here are not necessarily those of Notices. Responses on the Notices webpage are invited. Over the past three decades, the family of public-key In August 2015 the National Security Agency published cryptosystems, a fundamental breakthrough in modern a webpage announcing preliminary plans for transi- cryptography in the late 1970s, has become an increas- tioning to quantum-resistant algorithms (www.iad.gov /iad/programs/iad-initiatives/cnsa-suite.cfm). ingly integral part of our communication networks. The Gerrymandering is drawing political boundary lines with votes by your opponents and thus reduce your opponents’ In December 2016 the National Institute of Standards Internet, as well as other communication systems, relies an ulterior motive. This idea has great currency right now, share of seats relative to their share of the votes cast. and Technology (NIST) announced a call for proposals principally on the Diffie-Hellman key exchange, RSA with particular attention paid to manipulating shapes In this note we will focus on partisan gerry- for quantum-resistant algorithms with a deadline of 30 encryption, and digital signatures using DSA, ECDSA, or of US congressional and legislative districts in order to mandering. The Supreme Court has heard cases on November 2017 (www.nist.gov/pqcrypto). The effort related algorithms. -
Higher Chromatic Thom Spectra Via Unstable Homotopy Theory
HIGHER CHROMATIC THOM SPECTRA VIA UNSTABLE HOMOTOPY THEORY SANATH DEVALAPURKAR Abstract. We investigate implications of an old conjecture in unstable homotopy theory related to the Cohen-Moore-Neisendorfer theorem and a conjecture about the E2-topological Hochschild cohomology of certain Thom spectra (denoted A, B, and T (n)) related to Ravenel's X(pn). We show that these conjectures imply that the orientations MSpin → bo and MString → tmf admit spectrum-level splittings. This is shown by generalizing a theorem of Hopkins and Mahowald, which constructs HFp as a Thom spectrum, to construct BP⟨n − 1⟩, bo, and tmf as Thom spectra (albeit over T (n), A, and B respectively, and not over the sphere). This interpretation of BP⟨n − 1⟩, bo, and tmf offers a new perspective on Wood equivalences of the form bo ∧ Cη ≃ bu: they are related to the existence of certain EHP sequences in unstable homotopy theory. This construction of BP⟨n − 1⟩ also provides a different lens on the nilpotence theorem. Finally, we prove a C2-equivariant analogue of our construction, describing HZ as a Thom spectrum. Contents 1. Introduction 1 2. Background, and some classical positive and negative results5 3. Some Thom spectra 8 4. Review of some unstable homotopy theory 16 5. Chromatic Thom spectra 19 6. Applications 25 7. C2-equivariant analogue of CorollaryB 32 8. Future directions 35 References 36 1. Introduction 1.1. Statement of the main results. One of the goals of this paper is to describe a program to prove the following old conjecture (studied, for instance, in [Lau04, LS19], and discussed informally in many places, such as [MR09, Section 7]): Conjecture 1.1.1.