DOCSLIB.ORG

Mathematical Society ISSN 0002-9920

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Mathematical Society ISSN 0002-9920 Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Random Curves Number Story of the American Mathematical Society AVAILABLE Journeys of a From Counting to ONLINE April 2008 Volume 55, Number 4 Mathematician Cryptography N. Koblitz , University of P. M. Higgins , University Journal of Washington, Seattle, WA, of Essex, UK Geometric USA Numbers have fascinated These autobiographical people for centuries. They Analysis Mathematics and memoirs of Neal Koblitz, are familiar to everyone, coinventor of one of the two most popular forms forming a central pillar of our understanding of Editor-in-Chief: S. G. Krantz Voting of encryption and digital signature, cover many the world, yet the number system was not JGA is a high-quality journal devoted to topics besides his own personal career in presented to us “gift-wrapped” but, rather, was publishing important new results at the interface page 448 mathematics and cryptography - travels to the developed over millennia. Peter Higgins distills of analysis, geometry and partial diff erential Soviet Union, Latin America, Vietnam and centuries of work into one delightful narrative equations. Founded 17 years ago by its current elsewhere, political activism, and academic that celebrates the mystery of numbers and Editor-in-Chief, Steven G. Krantz, the journal has controversies relating to math education, the explains how diff erent kinds of numbers arose maintained standards of innovation and C. P. Snow two-culture problem, and mistreat- and why they are useful. Full of historical Henri’s Crystal Ball excellence. JGA accepts papers in English, French, ment of women in academia. snippets and interesting examples, the book and German and has a strong international fl avor. ranges from simple number puzzles and magic page 458 2008. X, 392 p. 28 illus., 18 in color. Hardcover tricks, to showing how ideas about numbers ISSN 1050-6926 (print) ISBN 978-3-540-74077-3 7 $49.95 relate to real-world problems. ISSN 1559-002X (electronic) Journal No. 12220 The Mathematical 2008. XII, 324 p. 33 illus. Hardcover Victor L. Klee 3RD ISBN 978-1-84800-000-1 7 $25.00 Theory of Finite EDITION Mathematical Element Methods 2ND (1925–2007) Universal Algebra Physiology EDITION S. C. Brenner, Louisiana ND G. Grätzer , University of 2 J. Keener, University of Utah, page 467 EDITION State University, Baton Rouge, LA, USA; Manitoba, Winnipeg, MB, Canada Salt Lake City, UT, USA; J. Sneyd , L. R. Scott, University of Chicago, IL, USA Massey University, Auckland, New Zealand; Universal Algebra has become the The book will be useful to mathematicians as most authoritative, consistently relied on text in Mathematical Physiology provides an well as engineers and physical scientists and can a fi eld with applications in other branches of introduction into physiology using the tools and be used for a course that provides an introduc- algebra as well as other fi elds such as combina- perspectives of mathematical modeling and tion to basic functional analysis, approximation torics, geometry and computer science. analysis. This second edition provides coverage theory, and numerical analysis, while building of more recent models in the chapters, more upon and applying basic techniques of real This second edition includes new appendices stochastic approaches, including single channel variable theory. This expanded third edition (with contributions from B. Jonnson, analysis and Fokker-Plank and Langevin contains new chapters on additive Schwarz R. Quackenbush, W. Taylor, and G. Wenzel) as well equations and includes new chapters on Calcium preconditioners and adaptive meshes, and new as an extensive bibliography of over 1,250 papers Dynamics, Neuroendocrine Cells and Regulation exercises have also been added throughout. and books. of Cell Function. 2nd ed. 1979. 2nd printing 2008. Approx. 605 p. Review of the Second Edition 7 [ is is] a well- Review of the First Edition 7 Probably the best Volume 55, Number 4, Pages 441–552, April 2008 10 illus. Softcover written book. A great deal of material is covered, book ever written on the subject of mathematical ISBN 978-0-387-77486-2 7 $79.95 and students who have taken the trouble to physiology....It contains numerous exercises, master at least some of the advanced material in enough to keep even the most diligent student the later chapters would be well placed to embark busy...highly recommended to anybody interested on research in the area. 7 ZENTRALBLATT MATH in mathematical or theoretical physiology. Mathematical Reviews 3rd ed. 2008. XVIII, 402 p. 50 illus. (Texts in Applied 7 Mathematics, Volume 15) Hardcover 2nd ed. 2008. Approx. 1000 p. Hardcover ISBN 978-0-387-75933-3 7 $69.95 ISBN 978-0-387-75846-6 7 approx. $100 Sign Up for New Book Alerts at springer.com Easy Ways to Order for the Americas 7 Write: Springer Order Department, PO Box 2485, Secaucus, NJ 07096-2485, USA 7 Call: (toll free) 1-800-SPRINGER 7 Fax: 1-201-348-4505 7 Email: [email protected] or for outside the Americas 7 Write: Springer Distribution Center GmbH, Haberstrasse 7, 69126 Heidelberg, Germany 7 Call: +49 (0) 6221-345-4301 7 Fax: +49 (0) 6221-345-4229 7 Email: [email protected] 7 Prices are subject to change without notice. All prices are net prices. 013575x Chaos in the weak stability boundary (see page 549) Trim: 8.25" x 10.75" 112 pages on 40 lb Cougar Opaque • Spine: 1/4" • Print Cover on 9pt Carolina ,!4%8 ,!4%8 ,!4%8 Pro New & Forthcoming from Birkhäuser Integrable Systems in Selfdual Gauge Field Vortices The Center and Cyclicity Celestial Mechanics An Analytical Approach Problems DIARMUID Ó MATHÚNA, Dublin Institute for Advanced GABRIELLA TARANTELLO, Università di Roma ‘Tor A Computational Approach Studies, Dublin, Ireland Vergata’, Italy VALERY ROMANOVSKI, University of Maribor, Slovenia; This work focuses on the two integrable systems of This monograph discusses specifi c examples DOUGLAS SHAFER, University of North Carolina at Charlotte, NC, USA relevance to celestial mechanics, both of which date of selfdual gauge fi eld structures, including the back to the 18th century. Under discussion are the Chern–Simons model, the abelian–Higgs model, and Using a computational algebra approach, this work Kepler (two-body) problem and the Euler (two-fi xed Yang–Mills gauge fi eld theory. addresses the center and cyclicity problems as center) problem, the latter being the more complex The author builds a foundation for gauge theory and behaviors of dynamical systems and families of and more instructive, as it exhibits a richer and more selfdual vortices by introducing the basic mathematical polynomial systems. The text fi rst lays the groundwork varied solution structure. language of gauge theory and formulating examples of for computational algebra and gives the main properties The present work shows that the solutions to all of Chern–Simons–Higgs theories (in both abelian and of ideals in polynomial rings and their affi ne varieties these integrable problems can be put in a form that non-abelian settings). Thereafter, the electroweak followed by a discussion on the theory of normal forms admits the general representation of the orbits and theory and self-gravitating electroweak strings are and stability. The center and cyclicity problems are follows a defi nite shared pattern. examined. The fi nal chapters treat elliptic problems then explored in detail. Containing exercises as well involving Chern–Simmons models, concentration- as historical notes and algorithms, this self-contained 2008/APPROX. 240 PP./HARDCOVER compactness principles, and Maxwell–Chern–Simons text is suitable for an advanced graduate course in the ISBN 9780817640965/$89.95 TENT. vortices. Many open questions still remain in the fi eld subject as well as a reference for researchers. PROGRESS IN MATHEMATICAL PHYSICS, VOL. 51 and are examined in this work in connection with Liouville-type equations and systems. 2008/APPROX. 300 PP., 5 ILLUS./SOFTCOVER ISBN 9780817647261/$59.95 TENT. The Theory of the Top The goal of this text is to form an understanding of Volume I: Introduction to the Kinematics selfdual solutions arising in a variety of physical and Kinetics of the Top contexts and thus is ideal for graduate students and Vanishing and Finiteness FELIX KLEIN; ARNOLD SOMMERFELD researchers interested in partial differential equations Results in Geometric Analysis and mathematical physics. Translated by: RAYMOND J. NAGEM and GUIDO SANDRI, A Generalization of the Bochner Technique both Boston University, Boston, MA, USA 2008/APPROX. 340 PP./HARDCOVER STEFANO PIGOLA, Università dell’Insubria, Como, Italy; ISBN 9780817643102/$109.00 MARCO RIGOLI, Università di Milano, Italy; The Theory of the Top, Vol. I is the fi rst of a series of PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS ALBERTO G. SETTI, Università dell’Insubria, Como, Italy four self-contained English translations of the classic AND THEIR APPLICATIONS, VOL. 72 and defi nitive treatment of rigid body motion. Volume I This book describes very recent results involving focuses on providing fundamental background material an extensive use of analytical tools in the study of and basic theoretical concepts. Integration and Modern geometrical and topological properties of complete Riemannian manifolds. An extension of the Bochner Key features: Analysis technique to the noncompact setting is analyzed in • Complete and unabridged presentation with recent JOHN J. BENEDETTO, University of Maryland, College detail, yielding conditions which ensure that solutions Park, USA; WOJCIECH CZAJA, University of Maryland, advances and additional notes College Park, USA of geometrically signifi cant differential equations either • Annotations by the translators provide insights into are trivial (vanishing results) or give rise to fi nite- the nature of science and mathematics in the late This textbook begins with the fundamentals of dimensional vector spaces (fi niteness results). 19th century classical real variables and leads to Lebesgue’s defi nition of the integral, the theory of integration 2008/APPROX.
Load more

Recommended publications
  • Kissing Numbers: Surprises in Dimension Four Günter M
    Kissing numbers: Surprises in Dimension Four Günter M. Ziegler, TU Berlin The “kissing number problem” is a basic geometric problem that got its name from billards: Two balls “kiss” if they touch. The kissing number problem asks how many other balls can touch one given ball at the same time. If you arrange the balls on a pool ta- ble, it is easy to see that the answer is exactly six: Six balls just perfectly surround a given ball. Graphic: Detlev Stalling, ZIB Berlin and at the same time Vladimir I. Levenstein˘ in Russia proved that the correct, exact maximal numbers for the kissing number prob- lem are 240 in dimension 8, and 196560 in dimension 24. This is amazing, because these are also the only two dimensions where one knows a precise answer. It depends on the fact that mathemati- cians know very remarkable configurations in dimensions 8 and 24, which they call the E8 lattice and the Leech lattice, respectively. If, however, you think about this as a three-dimensional problem, So the kissing number problem remained unsolved, in particular, the question “how many balls can touch a given ball at the same for the case of dimension four. The so-called 24-cell, a four- time” becomes much more interesting — and quite complicated. In dimensional “platonic solid” of remarkable beauty (next page), fact, The 17th century scientific genius Sir Isaac Newton and his yields a configuration of 24 balls that would touch a given one in colleague David Gregory had a controversy about this in 1694 — four-dimensional space.
    [Show full text]
  • LINEAR ALGEBRA METHODS in COMBINATORICS László Babai
    LINEAR ALGEBRA METHODS IN COMBINATORICS L´aszl´oBabai and P´eterFrankl Version 2.1∗ March 2020 ||||| ∗ Slight update of Version 2, 1992. ||||||||||||||||||||||| 1 c L´aszl´oBabai and P´eterFrankl. 1988, 1992, 2020. Preface Due perhaps to a recognition of the wide applicability of their elementary concepts and techniques, both combinatorics and linear algebra have gained increased representation in college mathematics curricula in recent decades. The combinatorial nature of the determinant expansion (and the related difficulty in teaching it) may hint at the plausibility of some link between the two areas. A more profound connection, the use of determinants in combinatorial enumeration goes back at least to the work of Kirchhoff in the middle of the 19th century on counting spanning trees in an electrical network. It is much less known, however, that quite apart from the theory of determinants, the elements of the theory of linear spaces has found striking applications to the theory of families of finite sets. With a mere knowledge of the concept of linear independence, unexpected connections can be made between algebra and combinatorics, thus greatly enhancing the impact of each subject on the student's perception of beauty and sense of coherence in mathematics. If these adjectives seem inflated, the reader is kindly invited to open the first chapter of the book, read the first page to the point where the first result is stated (\No more than 32 clubs can be formed in Oddtown"), and try to prove it before reading on. (The effect would, of course, be magnified if the title of this volume did not give away where to look for clues.) What we have said so far may suggest that the best place to present this material is a mathematics enhancement program for motivated high school students.
    [Show full text]
  • Gazette Des Mathématiciens
    JUILLET 2018 – No 157 la Gazette des Mathématiciens • Autour du Prix Fermat • Mathématiques – Processus ponctuels déterminantaux • Raconte-moi... le champ libre gaussien • Tribune libre – Quelle(s) application(s) pour le plan Torossian-Villani la GazetteComité de rédaction des Mathématiciens Rédacteur en chef Sébastien Gouëzel Boris Adamczewski Université de Nantes Institut Camille Jordan, Lyon [email protected] [email protected] Sophie Grivaux Rédacteurs Université de Lille [email protected] Thomas Alazard École Normale Supérieure de Paris-Saclay [email protected] Fanny Kassel IHÉS Maxime Bourrigan [email protected] Lycée Saint-Geneviève, Versailles [email protected] Pauline Lafitte Christophe Eckès École Centrale, Paris Archives Henri Poincaré, Nancy [email protected] [email protected] Damien Gayet Romain Tessera Institut Fourier, Grenoble Université Paris-Sud [email protected] [email protected] Secrétariat de rédaction : smf – Claire Ropartz Institut Henri Poincaré 11 rue Pierre et Marie Curie 75231 Paris cedex 05 Tél. : 01 44 27 67 96 – Fax : 01 40 46 90 96 [email protected] – http://smf.emath.fr Directeur de la publication : Stéphane Seuret issn : 0224-8999 À propos de la couverture. Cette image réalisée par Alejandro Rivera (Institut Fourier) est le graphe de la partie positive du champ libre gaussien sur le tore plat 2=(2á2) projeté sur la somme des espaces propres du laplacien de valeur propre plus petite que 500. Les textures et couleurs ajoutées sur le graphe sont pure- ment décoratives. La fonction a été calculée avec C++ comme une somme de polynômes trigonométriques avec des poids aléatoires bien choisis, le graphe a été réalisé sur Python et les textures et couleurs ont été réalisées avec gimp.
    [Show full text]
  • I. Overview of Activities, April, 2005-March, 2006 …
    MATHEMATICAL SCIENCES RESEARCH INSTITUTE ANNUAL REPORT FOR 2005-2006 I. Overview of Activities, April, 2005-March, 2006 …......……………………. 2 Innovations ………………………………………………………..... 2 Scientific Highlights …..…………………………………………… 4 MSRI Experiences ….……………………………………………… 6 II. Programs …………………………………………………………………….. 13 III. Workshops ……………………………………………………………………. 17 IV. Postdoctoral Fellows …………………………………………………………. 19 Papers by Postdoctoral Fellows …………………………………… 21 V. Mathematics Education and Awareness …...………………………………. 23 VI. Industrial Participation ...…………………………………………………… 26 VII. Future Programs …………………………………………………………….. 28 VIII. Collaborations ………………………………………………………………… 30 IX. Papers Reported by Members ………………………………………………. 35 X. Appendix - Final Reports ……………………………………………………. 45 Programs Workshops Summer Graduate Workshops MSRI Network Conferences MATHEMATICAL SCIENCES RESEARCH INSTITUTE ANNUAL REPORT FOR 2005-2006 I. Overview of Activities, April, 2005-March, 2006 This annual report covers MSRI projects and activities that have been concluded since the submission of the last report in May, 2005. This includes the Spring, 2005 semester programs, the 2005 summer graduate workshops, the Fall, 2005 programs and the January and February workshops of Spring, 2006. This report does not contain fiscal or demographic data. Those data will be submitted in the Fall, 2006 final report covering the completed fiscal 2006 year, based on audited financial reports. This report begins with a discussion of MSRI innovations undertaken this year, followed by highlights
    [Show full text]
  • Local Covering Optimality of Lattices: Leech Lattice Versus Root Lattice E8
    Local Covering Optimality of Lattices: Leech Lattice versus Root Lattice E8 Achill Sch¨urmann, Frank Vallentin ∗ 10th November 2004 Abstract We show that the Leech lattice gives a sphere covering which is locally least dense among lattice coverings. We show that a similar result is false for the root lattice E8. For this we construct a less dense covering lattice whose Delone subdivision has a common refinement with the Delone subdivision of E8. The new lattice yields a sphere covering which is more than 12% less dense than the formerly ∗ best known given by the lattice A8. Currently, the Leech lattice is the first and only known example of a locally optimal lattice covering having a non-simplicial Delone subdivision. We hereby in particular answer a question of Dickson posed in 1968. By showing that the Leech lattice is rigid our answer is even strongest possible in a sense. 1 Introduction The Leech lattice is the exceptional lattice in dimension 24. Soon after its discovery by Leech [Lee67] it was conjectured that it is extremal for several geometric problems in R24: the kissing number problem, the sphere packing problem and the sphere covering problem. In 1979, Odlyzko and Sloane and independently Levenshtein solved the kissing number problem in dimension 24 by showing that the Leech lattice gives an optimal solution. Two years later, Bannai and Sloane showed that it gives the unique solution up to isometries (see [CS88], Ch. 13, 14). Unlike the kissing number problem, the other two problems are still open. Recently, Cohn and Kumar [CK04] showed that the Leech lattice gives the unique densest lattice sphere packing in R24.
    [Show full text]
  • Abelian Solutions of the Soliton Equations and Riemann–Schottky Problems
    Russian Math. Surveys 63:6 1011–1022 c 2008 RAS(DoM) and LMS Uspekhi Mat. Nauk 63:6 19–30 DOI 10.1070/RM2008v063n06ABEH004576 Abelian solutions of the soliton equations and Riemann–Schottky problems I. M. Krichever Abstract. The present article is an exposition of the author’s talk at the conference dedicated to the 70th birthday of S. P. Novikov. The talk con- tained the proof of Welters’ conjecture which proposes a solution of the clas- sical Riemann–Schottky problem of characterizing the Jacobians of smooth algebraic curves in terms of the existence of a trisecant of the associated Kummer variety, and a solution of another classical problem of algebraic geometry, that of characterizing the Prym varieties of unramified covers. Contents 1. Introduction 1011 2. Welters’ trisecant conjecture 1014 3. The problem of characterization of Prym varieties 1017 4. Abelian solutions of the soliton equations 1018 Bibliography 1020 1. Introduction The famous Novikov conjecture which asserts that the Jacobians of smooth alge- braic curves are precisely those indecomposable principally polarized Abelian vari- eties whose theta-functions provide explicit solutions of the Kadomtsev–Petviashvili (KP) equation, fundamentally changed the relations between the classical algebraic geometry of Riemann surfaces and the theory of soliton equations. It turns out that the finite-gap, or algebro-geometric, theory of integration of non-linear equa- tions developed in the mid-1970s can provide a powerful tool for approaching the fundamental problems of the geometry of Abelian varieties. The basic tool of the general construction proposed by the author [1], [2]which g+k 1 establishes a correspondence between algebro-geometric data Γ,Pα,zα,S − (Γ) and solutions of some soliton equation, is the notion of Baker–Akhiezer{ function.} Here Γis a smooth algebraic curve of genus g with marked points Pα, in whose g+k 1 neighborhoods we fix local coordinates zα, and S − (Γ) is a symmetric prod- uct of the curve.
    [Show full text]
  • 1 Introduction 2 the Schottky Problem
    The Schottky problem and second order theta functions Bert van Geemen December Introduction The Schottky problem arose in the work of Riemann To a Riemann surface of genus g one can asso ciate a p erio d matrix which is an element of a space H of dimension g g Since the g Riemann surfaces themselves dep end on only g parameters if g the question arises as to how one can characterize the set of p erio d matrices of Riemann surfaces This is the Schottky problem There have b een many approaches and a few of them have b een succesfull All of them exploit a complex variety a ppav and a subvariety the theta divisor which one can asso ciate to a p oint in H When the p oint is the p erio d matrix of a Riemann surface this variety is g known as the Jacobian of the Riemann surface A careful study of the geometry and the functions on these varieties reveals that Jacobians and their theta divisors have various curious prop erties Now one attempts to show that such a prop erty characterizes Jacobians We refer to M Lectures III and IV for a nice exp osition of four such metho ds to vdG B D for overviews of later results and V for a newer approach In these notes we discuss a particular approach to the Schottky problem which has its origin the work of Schottky and Jung and unpublished work of Riemann It uses the fact that to a genus g curve one can asso ciate certain ab elian varieties of dimension g the Prym varieties In our presentation we emphasize an intrinsic line bundle on a ppav principally p olarized ab elian variety and the action
    [Show full text]
  • Breakthrough in My Favorite Open Problem of Mathematics: Chromatic Number of the Plane Alexander Soifer
    Breakthrough in My Favorite Open Problem of Mathematics: Chromatic Number of the Plane Alexander Soifer [I] can’t offer money for nice problems of other people because then I will really go broke… It is a very nice problem. If it were mine, I would offer $250 for it. – Paul Erdős Boca Raton, February 1992 1. Chromatic Number of the Plane: The Problem On behalf of all enthusiasts of this problem, let me express gratitude to my friend, the late Edward Nelson, who created this problem at a tender age of 18 in November 1950: What is the smallest number of colors sufficient for coloring the plane in such a way that no two points of the same color are unit distance apart? This number is called the chromatic number of the plane and is denoted by . In 1961, the Swiss geometer Hugo Hadwiger admitted that he was not the author of the problem, even though the name “Harwiger-Nelson” got stuck to the problem, just as Cardano did not author the Cardano Formula, and Pythagoras Theorem was known a millennium before the great Greek was born. Such is life with credits in mathematics. Right at problem’s birth, Eddie Nelson determined the lower bound of 4, and his 20-year old friend John Isbell, 20 figured out the upper bound of 7: = 4, or 5, or 6, or 7 A very broad spread. Which one is the value of ? Paul Erd"os thought 5. On May 28, 2009, during the DIMACS Ramsey Theory International Workshop that I organized on request of DIMACS Director Fred Roberts, I asked the distinguished audience to determine the chromatic number of the plane by democratic means of a vote.
    [Show full text]
  • Some Remarks on Even-Hole-Free Graphs
    Some remarks on even-hole-free graphs Zi-Xia Song∗ Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA Abstract A vertex of a graph is bisimplicial if the set of its neighbors is the union of two cliques; a graph is quasi-line if every vertex is bisimplicial. A recent result of Chudnovsky and Seymour asserts that every non-empty even-hole-free graph has a bisimplicial vertex. Both Hadwiger’s conjecture and the Erd˝os-Lov´asz Tihany conjecture have been shown to be true for quasi-line graphs, but are open for even-hole-free graphs. In this note, we prove that for all k ≥ 7, every even-hole-free graph with no Kk minor is (2k − 5)-colorable; every even-hole-free graph G with ω(G) < χ(G) = s + t − 1 satisfies the Erd˝os-Lov´asz Tihany conjecture provided that t ≥ s>χ(G)/3. Furthermore, we prove that every 9-chromatic graph G with ω(G) ≤ 8 has a K4 ∪ K6 minor. Our proofs rely heavily on the structural result of Chudnovsky and Seymour on even-hole-free graphs. 1 Introduction All graphs in this paper are finite and simple. For a graph G, we use V (G) to denote the vertex set, E(G) the edge set, |G| the number of vertices, e(G) the number of edges, δ(G) the minimum degree, ∆(G) the maximum degree, α(G) the independence number, ω(G) the clique number and χ(G) the chromatic number. A graph H is a minor of a graph G if H can be obtained from a subgraph of G by contracting edges.
    [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]
  • BIRS 2010 Scientific Report
    Banff International Research Station for Mathematical Innovation and Discovery 2010 Scientific Report 5-Day Workshops 2010 Jan 10 Jan 15 Mathematics and Physics of Polymer Entanglement Jan 17 Jan 22 Multi-Scale Stochastic Modeling of Cell Dynamics Jan 24 Jan 29 Sparse Random Structures: Analysis and Computation Jan 31 Feb 5 Theory and Applications of Matrices Described by Patterns Jan 31 Feb 5 Branching Random Walks and Searching in Trees Feb 7 Feb 12 Small-scale Hydrodynamics: Microfluidics and Thin Films Feb 14 Feb 19 Convex Algebraic Geometry Feb 21 Feb 26 Some Mathematical Problems of Material Science Feb 28 Mar 5 Randomization, Relaxation and Complexity Mar 7 Mar 12 Quasi-Isometric Rigidity in Low-Dimensional Topology Mar 7 Mar 12 (0,2) Mirror Symmetry and Heterotic Gromov-Witten Invariants Mar 14 Mar 19 Geometric Scattering Theory and Applications Mar 21 Mar 26 Deterministic and Stochastic Front Propagation Mar 28 Apr 2 Volume Inequalities Apr 4 Apr 9 Coordinated Mathematical Modeling of Internal Waves Apr 11 Apr 16 Generalized Complex and Holomorphic Poisson Geometry Apr 18 Apr 23 Optimal Transportation and Applications Apr 25 Apr 30 Character Varieties in the Geometry and Topology of Low-Dimensional Manifolds May 2 May 7 Functional Data Analysis: Future Directions May 2 May 7 Creative Writing in Mathematics and Science May 9 May 14 Nonlinear Diffusions and Entropy Dissipation: From Geometry to Biology May 16 May 21 Inverse Transport Theory and Tomography May 23 May 28 Self-assembly of Block Copolymers: Theoretical Models and Mathematical
    [Show full text]
  • Gauss-Manin Connection in Disguise: Calabi-Yau Threefolds 1
    Gauss-Manin connection in disguise: Calabi-Yau threefolds 1 Murad Alim, Hossein Movasati, Emanuel Scheidegger, Shing-Tung Yau Abstract We describe a Lie Algebra on the moduli space of Calabi-Yau threefolds enhanced with differential forms and its relation to the Bershadsky-Cecotti-Ooguri-Vafa holo- morphic anomaly equation. In particular, we describe algebraic topological string alg partition functions Fg , g ≥ 1, which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck’s algebraic de Rham cohomology and on the algebraic Gauss-Manin connection. In this way, we recover a result of Yamaguchi-Yau and Alim-L¨ange in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi-Yau threefolds cor- respond to coordinates on such a moduli space. We discuss the mirror quintic as an example. Contents 1 Introduction 2 2 Holomorphic anomaly equations 7 2.1 Specialgeometry ................................. 7 2.2 Specialcoordinates.............................. 8 2.3 Holomorphic anomaly equations . ... 9 2.4 Polynomialstructure. .. .. .. .. .. .. .. .. 9 3 Algebraic structure of topological string theory 10 3.1 Specialpolynomialrings . 10 3.2 Different choices of Hodge filtrations . ..... 12 3.3 LieAlgebradescription . 13 3.4 Algebraic master anomaly equation . ..... 14 arXiv:1410.1889v1 [math.AG] 7 Oct 2014 4 Proofs 15 4.1 Generalizedperioddomain . 15 4.2 ProofofTheorem1................................ 16 4.3 ProofofTheorem2................................ 17 4.4 The Lie Algebra G ................................ 18 4.5 Two fundamental equalities of the special geometry . .......... 18 5 Mirror quintic case 19 6 Final remarks 21 1 Math.
    [Show full text]