DOCSLIB.ORG

Mathematical Physics, Analysis and Geometry

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Mathematical Physics, Analysis and Geometry ISSN 0002-9920 of the American Mathematical Society February 2001 Volume 48, Number 2 Mathematics for Teaching page 168 0 2 0 1 1 Honeycombs and 2 Sums of Hermitian 2 0 Matrices page 175 -3,-3 0 Lawrence Meeting -2,-2,-2 page 276 Las Vegas Meeting page 278 2 2 Hoboken Meeting page 280 -3 -2 -1 -4 -1,-1 2 0 2 0 -4 -2 0 -3 -2 -1 Honeycombs and Tensor Products (see page 186) The ' frl~ te igra·H~n ofrMatfT Type~ett ·rng and-CoFripufer Algebra 'I '\':. l_t •\ \ ,J_! \. Sci e The Gold Standard for Mathematical Publishing and the Easiest-to-Use Computer Algebra System Scientific WorkPlace makes writing and doing mathematics easier than you ever imagined possible. Because Scientific WorkPlace thinks like you do, you can compose and edit your documents directly on the screen, without being forced to think in a programming language. A simple click of a button allows you to typeset your document in lbTE)C . This lets you concentrate on creating a correct paper, while Scientific WorkPlace ensures that it is a beautiful one. With Scientific WorkPlace, you can also compute and plot solutions with the integrated computer algebra system. Increase Your Productivity Scientific WorkPlace enables both professional and support staff to produce stunning results quickly and easily, without having to know TEX™, lbTEX, or computer algebra syntax. And, as an added benefit, MacKichan Software provides free, prompt, and knowledgeable technical support. Visit our homepage for free evaluation copies of all our software. cKichan SOFTWARE, INC . Email: info@mackichan .com • Toll Free: 877-724-9673 • Fax: 206-780-2857 MacKichan Software, Inc. • 600 Ericksen Ave. NE, Suite 300 • Bainbridge Island, WA 98110 www.mackichan.com/notices Tools for Scientific Creativity Since /98/ AMERICAN MATHEMATICAL SOCIETY New Titles from the AMS Laminations and Foliations in Geometry, Supplementary Readmg Topology, and Dynamics Partial Differential Equations in Several Mikhail Lyubich, John W. Milnor, and Yair N. Minsky, SUNY at Complex Variables Stony Brook, NY, Editors So-Chin Chen, National Tsing-Hua University, Hsinchu, Taiwan, This volume is based on a conference held at SUNY, Stony Brook and Mei-Chi Shaw, University of Notre Dame, IN (NY). The concepts of laminations and foliations appear in a diverse This book is intended as both an introductory text and a reference number of fields, such as topology, geometry, analytic differential book for those interested in studying several complex variables in the equations, holomorphic dynamics, and renormalization theory. context of partial differential equations. In the last few decades, signif­ Although these areas have developed deep relations, each has devel­ icant progress was made in the study of Cauchy-Riemann and oped distinct research fields with little interaction among practitioners. tangential Cauchy-Riemann operators; this progress greatly influ­ The conference brought together the diverse points of view of enced the development of PDEs and several complex variables. After researchers from different areas. This book includes surveys and the background material in complex analysis is developed in research papers reflecting the broad spectrum of themes presented Chapters 1 through 3, the next three chapters are devoted to the at the event. solvability and regularity of the Cauchy-Riemann equations using Contemporary Mathematics, Volume 269; 2001 ; approximately 232 Hilbert space techniques. The second part of the book gives a pages; Softcover; ISBN 0-8218-1985-2; List $59; Individual member $35; comprehensive study of the tangential Cauchy-Riemann equations, Order code CONM/269NT102 another important class of equations in several complex variables first studied by Lewy. Embeddability of abstract CR structures is Recommended Text discussed in detail here for the first time. Algebraic Geometry 2 This fairly self-contained book provides a much-needed introductory Sheaves and Cohomology text. It also provides a rich source of information to experts. Kenji Ueno, Kyoto University, Japan Titles in this series are copublished with International Press, Cambridge, MA. Modern algebraic geometry is built upon two fundamental notions: AMsnP Studies In Advanced Mathematics, Volume 19; 2001 ; 380 schemes and sheaves. The theory of schemes was explained in pages; Hardcover; ISBN D-8218-1062 -6; List $49; All AMS members $39; Algebraic Geometry 1: From Algebraic Varieties to Schemes (see Order code AMSIP/19NT102 Volume 185 in the same series, Translations of Mathematical Monographs). In the present book, Ueno turns to the theory of Topics in Functional Differential and sheaves and their cohomology. Loosely speaking, a sheaf is a way of Difference Equations keeping track of local information defined on a topological space, Teresa Faria, Universidade de Lisboa, Portugal, and such as the local holomorphic functions on a complex manifold or the Pedro Freitas, lnstituto Superior Tecnico, Lisboa, Portugal, local sections of a vector bundle. To study schemes, it is useful to Editors study the sheaves defined on them, especially the coherent and This volume contains papers written by participants at the quasicoherent sheaves. The primary tool in understanding sheaves is Conference on Functional Differential and Difference Equations held cohomology. For example, in studying ampleness, it is frequently a statement about its at the lnstituto Superior Tecnico in Lisbon, Portugal. The conference useful to translate a property of sheaves into brought together mathematicians working in a wide range of topics, cohomology. including qualitative properties of solutions, bifurcation and stability The text covers the important topics of sheaf theory, including types theory, oscillatory behavior, control theory and feedback systems, of sheaves and the fundamental operations on them, such as ... biological models, state-dependent delay equations, Lyapunov • coherent and quasicoherent sheaves. methods, etc. Articles are written by leading experts in the field. A • proper and projective morphisms. comprehensive overview is given of these active areas of research. • ~irect and inverse images. • Cech cohomology. Fields Institute Communications, Volume 29; 2001 ; 378 pages; Hardcover; ISBN 0-8218-2701-4; List $11 0; Individual member $66; Order For the mathematician unfamiliar with the language of schemes and code FIC/29NT1 02 sheaves, algebraic geometry can seem distant. However, Ueno makes the topic seem natural through his concise style and his Operator Theoretical Methods insightful explanations. He explains why things are done this way and A. Gheondea, R. N. Gologan, and D. Timotin, Romanian supplements his explanations with illuminating examples. As a result, Academy, Bucharest, Editors he is able to make algebraic geometry very accessible to a wide A publication of the Theta Foundation. audience of non-specialists. This volume contains carefully selected contributions by participants The book contains numerous problems and exercises with solutions. at the Seventeenth International Conference on Operator Theory held It would be an excellent text for the second part of a course in alge­ braic geometry. at the University of Timi~ara (Romania). A large variety of topics are covered, including single operator theory, C* -algebras, spectral Translations of Mathematical Monographs (lwanami Series in Modern theory, special classes of concrete operators, and holomorphic oper­ Mathematics), Volume 197; 2001 ; approximately 200 pages; Softcover; ator functions. The book also includes applications in other areas of ISBN 0-8218·1357 -9; List $29; All AMS members $23; Order code mathematics and science. MMON0/197NT1 02 Distributed worldwide, except in Romania, by the AMS. International Book Series of Mathematical Texts; 2000; 415 pages; Hardcover; ISBN 973-99097-2-8; List $38; All AMS members $30; Order code THETA/1NT102 ~CJN'oEO \~ AMS AMERICAN MATHEMATICAL SocmTY All prices subject to change. Charges for delivery are $3.00 per order. For optional air delivery outside of the continental U. S., please include $6.50 per item. Prepayment required. Order from: American Mathematical Society, P. 0. Box 845904, Boston, MA 02284-5904, USA. For credit card orders, fax 1-401-455-4046 or call toll free 1-800-321-4AMS (4267) in the U. S. and Canada, 1-401-455-4000 worldwide. Or place your order through the AMS Bookstore at www.ams.org/bookstore. Residents of Canada, please include 7%GS T. Electrodynamics A Modem Geometric Approach W.E. Baylis, University of Windsor, ON, Canada "[The book} has a nice blend of mathematical physics, fundamentals of electromagnetic theory and practical applications ... It is extremely well written and contains numerous exercises and problems to help the reader gain familiarity with new concepts. Throughout ... the author emphasizes the conceptual framework of electromagnet­ ism so that the reader does not get lost in details. Such a Relaunch! style is very valuable in a physics textbook ... The book simultaneously teaches the reader electromagnetic theory Progress In Mathematical Physics and more advanced mathematical concepts in a very Progress in Mathematical Physics (formerly Progress in Physics) is a book series encompassing all areas of concrete physical context ... Essentially self-contained.. mathematical physics. It is intended for mathematicians, physicists, and other scientists, as well as graduate it will serve as an excellent textbook for graduate level students in the above related areas. This distinguished collection of books includes
Load more

Recommended publications
  • Ζ−1 Using Theorem 1.2
    UC San Diego UC San Diego Electronic Theses and Dissertations Title Ihara zeta functions of irregular graphs Permalink https://escholarship.org/uc/item/3ws358jm Author Horton, Matthew D. Publication Date 2006 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA, SAN DIEGO Ihara zeta functions of irregular graphs A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Mathematics by Matthew D. Horton Committee in charge: Professor Audrey Terras, Chair Professor Mihir Bellare Professor Ron Evans Professor Herbert Levine Professor Harold Stark 2006 Copyright Matthew D. Horton, 2006 All rights reserved. The dissertation of Matthew D. Horton is ap- proved, and it is acceptable in quality and form for publication on micro¯lm: Chair University of California, San Diego 2006 iii To my wife and family Never hold discussions with the monkey when the organ grinder is in the room. |Sir Winston Churchill iv TABLE OF CONTENTS Signature Page . iii Dedication . iv Table of Contents . v List of Figures . vii List of Tables . viii Acknowledgements . ix Vita ...................................... x Abstract of the Dissertation . xi 1 Introduction . 1 1.1 Preliminaries . 1 1.2 Ihara zeta function of a graph . 4 1.3 Simplifying assumptions . 8 2 Poles of the Ihara zeta function . 10 2.1 Bounds on the poles . 10 2.2 Relations among the poles . 13 3 Recovering information . 17 3.1 The hope . 17 3.2 Recovering Girth . 18 3.3 Chromatic polynomials and Ihara zeta functions . 20 4 Relations among Ihara zeta functions .
    [Show full text]
  • Ihara Zeta Functions
    Audrey Terras 2/16/2004 fun with zeta and L- functions of graphs Audrey Terras U.C.S.D. February, 2004 IPAM Workshop on Automorphic Forms, Group Theory and Graph Expansion Introduction The Riemann zeta function for Re(s)>1 ∞ 1 −1 ζ ()sp== 1 −−s . ∑ s ∏ () n=1 n pprime= Riemann extended to all complex s with pole at s=1. Functional equation relates value at s and 1-s Riemann hypothesis duality between primes and complex zeros of zeta See Davenport, Multiplicative Number Theory. 1 Audrey Terras 2/16/2004 Graph of |Zeta| Graph of z=| z(x+iy) | showing the pole at x+iy=1 and the first 6 zeros which are on the line x=1/2, of course. The picture was made by D. Asimov and S. Wagon to accompany their article on the evidence for the Riemann hypothesis as of 1986. A. Odlyzko’s Comparison of Spacings of Zeros of Zeta and Eigenvalues of Random Hermitian Matrix. See B. Cipra, What’s Happening in Math. Sciences, 1998-1999. 2 Audrey Terras 2/16/2004 Dedekind zeta of an We’ll algebraic number field F, say where primes become prime more ideals p and infinite product of about number terms field (1-Np-s)-1, zetas Many Kinds of Zeta Np = norm of p = #(O/p), soon O=ring of integers in F but not Selberg zeta Selberg zeta associated to a compact Riemannian manifold M=G\H, H = upper half plane with arc length ds2=(dx2+dy2)y-2 , G=discrete group of real fractional linear transformations primes = primitive closed geodesics C in M of length −+()()sjν C ν(C), Selberg Zs()=− 1 e (primitive means only go Zeta = ∏ ∏( ) around once) []Cj≥ 0 Reference: A.T., Harmonic Analysis on Symmetric Duality between spectrum ∆ on M & lengths closed geodesics in M Spaces and Applications, I.
    [Show full text]
  • Notices of the American Mathematical Society
    • ISSN 0002-9920 March 2003 Volume 50, Number 3 Disks That Are Double Spiral Staircases page 327 The RieITlann Hypothesis page 341 San Francisco Meeting page 423 Primitive curve painting (see page 356) Education is no longer just about classrooms and labs. With the growing diversity and complexity of educational programs, you need a software system that lets you efficiently deliver effective learning tools to literally, the world. Maple® now offers you a choice to address the reality of today's mathematics education. Maple® 8 - the standard Perfect for students in mathematics, sciences, and engineering. Maple® 8 offers all the power, flexibility, and resources your technical students need to manage even the most complex mathematical concepts. MapleNET™ -- online education ,.u A complete standards-based solution for authoring, nv3a~ _r.~ .::..,-;.-:.- delivering, and managing interactive learning modules \~.:...br *'r¥'''' S\l!t"AaITI(!\pU;; ,"", <If through browsers. Derived from the legendary Maple® .Att~~ .. <:t~~::,/, engine, MapleNefM is the only comprehensive solution "f'I!hlislJer~l!'Ct"\ :5 -~~~~~:--r---, for distance education in mathematics. Give your institution and your students cornpetitive edge. For a FREE 3D-day Maple® 8 Trial CD for Windows®, or to register for a FREE MapleNefM Online Seminar call 1/800 R67.6583 or e-mail [email protected]. ADVANCING MATHEMATICS WWW.MAPLESOFT.COM I [email protected]\I I WWW.MAPLEAPPS.COM I NORTH AMERICAN SALES 1/800 267. 6583 © 2003 Woter1oo Ma')Ir~ Inc Maple IS (J y<?glsterc() crademork of Woterloo Maple he Mar)leNet so troc1ema'k of Woter1oc' fV'lop'e Inr PII other trcde,nork$ (ye property o~ their respective ('wners Generic Polynomials Constructive Aspects of the Inverse Galois Problem Christian U.
    [Show full text]
  • The Missing Boundaries of the Santaló Diagrams for the Cases (D
    Discrete Comput Geom 23:381–388 (2000) Discrete & Computational DOI: 10.1007/s004540010006 Geometry © 2000 Springer-Verlag New York Inc. The Missing Boundaries of the Santal´o Diagrams for the Cases (d,ω,R) and (ω, R, r) M. A. Hern´andez Cifre and S. Segura Gomis Departamento de Matem´aticas, Universidad de Murcia, 30100 Murcia, Spain {mhcifre,salsegom}@fcu.um.es Abstract. In this paper we solve two open problems posed by Santal´o: to obtain complete systems of inequalities for some triples of measures of a planar convex set. 1. Introduction There is abundant literature on geometric inequalities for planar figures. These inequali- ties connect several geometric quantities and in many cases determine the extremal sets which satisfy the equality conditions. Each new inequality obtained is interesting on its own, but it is also possible to ask if a collection of inequalities concerning several geometric magnitudes is large enough to determine the existence of the figure. Such a collection is called a complete system of inequalities: a system of inequalities relating all the geometric characteristics such that, for any set of numbers satisfying those conditions, a planar figure with these values of the characteristics exists in the given class. Santal´o [7] considered the area, the perimeter, the diameter, the minimal width, the circumradius, and the inradius of a planar convex K (A, p, d, ω, R and r, respectively). He tried to find complete systems of inequalities concerning either two or three of these measures. He found that, for pairs of measures, the known classic inequalities between them already form a complete system.
    [Show full text]
  • Graphs: Random, Chaos, and Quantum
    Graphs: Random, Chaos, and Quantum Matilde Marcolli Fields Institute Program on Geometry and Neuroscience and MAT1845HS: Introduction to Fractal Geometry and Chaos University of Toronto, March 2020 Matilde Marcolli Graphs: Random, Chaos, and Quantum Some References Alex Fornito, Andrew Zalesky, Edward Bullmore, Fundamentals of Brain Network Analysis, Elsevier, 2016 Olaf Sporns, Networks of the Brain, MIT Press, 2010 Olaf Sporns, Discovering the Human Connectome, MIT Press, 2012 Fan Chung, Linyuan Lu, Complex Graphs and Networks, American Mathematical Society, 2004 L´aszl´oLov´asz, Large Networks and Graph Limits, American Mathematical Society, 2012 Matilde Marcolli Graphs: Random, Chaos, and Quantum Graphs G = (V ; E;@) • V = V (G) set of vertices (nodes) • E = E(G) set of edges (connections) • boundary map @ : E(G) ! V (G) × V (G), boundary vertices @(e) = fv; v 0g • directed graph (oriented edges): source and target maps s : E(G) ! V (G); t : E(G) ! V (G);@(e) = fs(e); t(e)g • looping edge: s(e) = t(e) starts and ends at same vertex; parallel edges: e 6= e0 with @(e) = @(e0) • simplifying assumption: graphs G with no parallel edges and no looping edges (sometimes assume one or the other) • additional data: label functions fV : V (G) ! LV and fE : E(G) ! LE to sets of vertex and edge labels LV and LE Matilde Marcolli Graphs: Random, Chaos, and Quantum Examples of Graphs Matilde Marcolli Graphs: Random, Chaos, and Quantum Network Graphs (Example from Facebook) Matilde Marcolli Graphs: Random, Chaos, and Quantum Increasing Randomness rewiring
    [Show full text]
  • Finite Models for Arithmetical Quantum Chaos
    Finite Models for Arithmetical Quantum Chaos Audrey Terras Math. Dept., U.C.S.D., San Diego, Ca 92093-0112 Abstract. Physicists have long studied spectra of Schrödinger operators and random matrices thanks to the implications for quantum mechanics. Analo- gously number theorists and geometers have investigated the statistics of spec- tra of Laplacians on Riemannian manifolds. This has been termed by Sarnak “arithmetic quantum chaos” when the manifolds are quotients of a symmet- ric space modulo an arithmetic group such as the modular group SL(2, Z). Equivalently one seeks the statistics of the zeros of Selberg zeta functions. Parallels with the statistics of the zeros of the Riemann zeta function have been evident to physicists for some time. Here we survey what may be called “finite quantum chaos” seeking connections with the continuous theory. We will also discuss discrete analogue of Selberg’s trace formula as well as Ihara zeta functions of graphs. Part 1 Lecture 1. Finite Models 1. Introduction This is a story of a tree related to the spectral theory of operators on Hilbert spaces. The tree has three branches as in Figure 1. The left branch is that of quantum physics: the statistics of energy levels of quantum mechanical systems; i.e. the eigenvalues of the Schrödinger operator φn = λnφn. The middle branch is that of geometry and number theory. In the middleL we see the spectrum of the Laplace operator = ∆ on a Riemannian manifold M such as the fundamental L domain of the modular group SL(2, Z) of 2 2 integer matrices with determinant 1.
    [Show full text]
  • THE A·B·C·Ds of SCHUBERT CALCULUS
    THE A·B·C·Ds OF SCHUBERT CALCULUS COLLEEN ROBICHAUX, HARSHIT YADAV, AND ALEXANDER YONG ABSTRACT. We collect Atiyah-Bott Combinatorial Dreams (A·B·C·Ds) in Schubert calculus. One result relates equivariant structure coefficients for two isotropic flag manifolds, with consequences to the thesis of C. Monical. We contextualize using work of N. Bergeron- F. Sottile, S. Billey-M. Haiman, P. Pragacz, and T. Ikeda-L. Mihalcea-I. Naruse. The relation complements a theorem of A. Kresch-H. Tamvakis in quantum cohomology. Results of A. Buch-V. Ravikumar rule out a similar correspondence in K-theory. 1. INTRODUCTION 1.1. Conceptual framework. Each generalized flag variety G=B has finitely many orbits under the left action of the (opposite) Borel subgroup B− of a complex reductive Lie group ∼ G. They are indexed by elements w of the Weyl group W = N(T)=T, where T = B \ B− is a maximal torus. The Schubert varieties are closures Xw of these orbits. The Poincare´ duals ? of the Schubert varieties fσwgw2W form a Z-linear basis of the cohomology ring H (G=B). The Schubert structure coefficients are nonnegative integers, defined by X w σu ` σv = cu;vσw: w2W w Geometrically, cu;v 2 Z≥0 counts intersection points of generic translates of three Schubert varieties. The main problem of modern Schubert calculus is to combinatorially explain this positivity. For Grassmannians, this is achieved by the Littlewood-Richardson rule [13]. The title alludes to a principle, traceable to M. Atiyah-R. Bott [6], that equivariant coho- mology is a lever on ordinary cohomology.
    [Show full text]
  • Quantum Chaos on Discrete Graphs 2
    Quantum chaos on discrete graphs Uzy Smilansky Department of Physics of Complex Systems, The Weizmann Institute of Science, Rehovot 76100, Israel. and Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH, UK. E-mail: [email protected] Abstract. Adapting a method developed for the study of quantum chaos on quantum (metric) graphs [1], spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph, and obtaining functions which belongs to the class of ζ functions proposed originally by Ihara [2], and expanded by subsequent authors [3, 4]. Finally, a model of “classical dynamics” on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs [1]. arXiv:0704.3525v1 [math-ph] 26 Apr 2007 1. Introduction and preliminaries Some ten years ago quantum (metric) graphs were proposed as a convenient paradigm for the study of quantum chaos in compact [1] and scattering [5] systems. The crucial point which highlighted the close similarity between metric graphs - whose only claim to complexity is their topology - and chaotic Hamiltonian flows is the formal similarity between the trace formulae [6, 7] which express the spectral densities as sums over periodic orbits. Requiring additionally that the lengths of the bonds are rationally independent, and that the graph is well connected, render the spectrum of Quantum chaos on discrete graphs 2 the Schr¨odinger operator on graphs sufficiently disordered to display spectral statistics which are consistent with the predictions of Random Matrix Theory.
    [Show full text]
  • Lectures on the Mathematics of Quantum Mechanics Volume II: Selected Topics
    Gianfausto Dell'Antonio Lectures on the Mathematics of Quantum Mechanics Volume II: Selected Topics February 17, 2016 Mathematical Department, Universita' Sapienza (Rome) Mathematics Area, ISAS (Trieste) 2 A Caterina, Fiammetta, Simonetta Il ne faut pas toujours tellement epuiser un sujet q'on ne laisse rien a fair au lecteur. Il ne s'agit pas de fair lire, mais de faire penser Charles de Secondat, Baron de Montesquieu Contents 1 Lecture 1. Wigner functions. Coherent states. Gabor transform. Semiclassical correlation functions ........................ 11 1.1 Coherent states . 15 1.2 Husimi distribution . 17 1.3 Semiclassical limit using Wigner functions . 21 1.4 Gabor transform . 24 1.5 Semiclassical limit of joint distribution function . 25 1.6 Semiclassical limit using coherent states . 26 1.7 Convergence of quantum solutions to classical solutions . 29 1.8 References for Lecture 1 . 34 2 Lecture 2 Pseudifferential operators . Berezin, Kohn-Nirenberg, Born-Jordan quantizations ................................. 35 2.1 Weyl symbols . 36 2.2 Pseudodifferential operators . 36 2.3 Calderon - Vaillantcourt theorem . 39 2.4 Classes of Pseudodifferential operators. Regularity properties. 44 2.5 Product of Operator versus products of symbols . 46 2.6 Correspondence between commutators and Poisson brackets; time evolution . 49 2.7 Berezin quantization . 51 2.8 Toeplitz operators . 53 2.9 Kohn-Nirenberg Quantization . 54 2.10 Shubin Quantization . 55 2.11 Born-Jordarn quantization . 56 2.12 References for Lecture 2 . 57 4 Contents 3 Lecture 3 Compact and Schatten class operators. Compactness criteria. Bouquet of Inequalities ........................... 59 3.1 Schatten Classes . 64 3.2 General traces . 65 3.3 General Lp spaces .
    [Show full text]
  • Ransactions of The
    VOLUME328 NUMBER 2 EI 11999 DECEMBER1991 RANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY EDITED BY Avner D. Ash James E. Baumgartner James W. Cannon Sun-Yung A. Chang Ralph Cohen Richard Durrett David Jerison Jerry L. Kazdan Roger D. Nussbaum Carl Pomerance Judith D. Sally David J. Saltman, Managing Editor Masamichi Takesaki Audrey Terras PROVIDENCE. RHODE ISLAND USA TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY THIS JOURNAL is devoted entirely to research in pure and applied mathematics, and includes, in general, longer papers than those in the PROCEEDINGS. Papers should be at least 16 typed pages in length. PREPARATION OF THE MANUSCRIPT. All papers should be typewritten double-spaced, and two copies should be sent to the appropriate editor. The author should keep a complete copy. To encourage the submission of manuscripts in electronic form using TgX and the ^xS-TgX macro package, the Executive Committee of the Council has adopted a policy that allows for accelerating the publication date of such manuscripts by as much as 20 weeks, which is approximately equal to the time normally needed by the Society for copyediting, typesetting, and proofreading an average manuscript. FORM OF MANUSCRIPT. The first page should consist of a descriptive title, followed by an abstract which summarizes the article in language suitable for workers in the general field (algebra, analysis, etc.). "Some The descriptive title should be short, but informative; useless or vague phrases such as remarks "concerning" about" or should be avoided. Also avoid proper names unless mathematical usage associates them with the work. The abstract should be at least one complete sentence, and at most 300 words, with the upper limit primarily for longer papers.
    [Show full text]
  • 2021 September-October Newsletter
    Newsletter VOLUME 51, NO. 5 • SEPTEMBER–OCTOBER 2021 PRESIDENT’S REPORT This is a fun report to write, where I can share news of AWM’s recent award recognitions. Sometimes hearing about the accomplishments of others can make The purpose of the Association for Women in Mathematics is us feel like we are not good enough. I hope that we can instead feel inspired by the work these people have produced and energized to continue the good work we • to encourage women and girls to ourselves are doing. study and to have active careers in the mathematical sciences, and We’ve honored exemplary Student Chapters. Virginia Tech received the • to promote equal opportunity and award for Scientific Achievement for offering three different research-focused the equal treatment of women and programs during a pandemic year. UC San Diego received the award for Professional girls in the mathematical sciences. Development for offering multiple events related to recruitment and success in the mathematical sciences. Kutztown University received the award for Com- munity Engagement for a series of events making math accessible to a broad community. Finally, Rutgers University received the Fundraising award for their creative fundraising ideas. Congratulations to all your members! AWM is grateful for your work to support our mission. The AWM Research Awards honor excellence in specific research areas. Yaiza Canzani was selected for the AWM-Sadosky Research Prize in Analysis for her work in spectral geometry. Jennifer Balakrishnan was selected for the AWM- Microsoft Research Prize in Algebra and Number Theory for her work in computa- tional number theory.
    [Show full text]
  • Sparse Bounds in Harmonic Analysis and Semiperiodic Estimates
    Sparse Bounds in Harmonic Analysis and Semiperiodic Estimates by Alexander Barron May 2019 2 c Copyright 2019 by Alexander Barron i This dissertation by Alex Barron is accepted in its present form by the Department of Mathematics as satisfying the dissertation requirement for the degree of Doctor of Philosophy Date Jill Pipher, Ph.D., Advisor Recommended to the Graduate Council Date Benoit Pausader, Ph.D., Reader Date Sergei Treil, Ph.D., Reader Approved by the Graduate Council Date Andrew G. Campbell, Dean of the Graduate School ii Vitae Alexander Barron graduated from Colby College with a B.A. in Mathematics in May 2013 (summa cum laude, Phi Beta Kappa). He also earned an M.S. in mathematics from Brown University in May 2016. At Brown he was a teaching assistant and instructor for multiple sections of Calculus I and II, and also for multivariable calculus. He has given research talks at various conferences and institutions, including Georgia Tech, the University of Virginia, the University of New Mexico, and the American Institute of Math (AIM). Starting in August 2019 he will be serving as a Doob Visiting Assistant Professor at the University of Illinois Urbana- Champaign. Below is a list of publications and preprints by the author. 1. Weighted Estimates for Rough Bilinear Singular Integrals via Sparse Domination, N.Y. Journal of Math 23 (2017) 779-811. 2. Sparse bounds for bi-parameter operators using square functions, with Jill Pipher. Preprint arXiv:1709.05009. 3. Sparse domination and the strong maximal function, with Jos´eConde Alonso, Yumeng Ou, and Guillermo Rey.
    [Show full text]