ISSN 0002-9920 Notices of the American Mathematical Society of the American Mathematical Society October 2010 Volume 57, Number 9 Topological Methods What if Newton saw an apple as just an apple? for Nonlinear Oscillations page 1080 Tilings, Scaling Functions, and a Markov Process page 1094 Reminiscences of Grothendieck and His School page 1106 Speaking with the Would we have his laws of gravity? That’s the power Natives: Refl ections of seeing things in different ways. When it comes to on Mathematical TI technology, look beyond graphing calculators. Communication ™ ® Think TI-Nspire Computer Software for PC or Mac . page 1121 » Software that’s easy to use. Explore higher order mathematics and dynamically connected represen- Volume 57, Number 9, Pages 1073–1240, October 2010 New Orleans Meeting tations on a highly intuitive, full-color user interface. page 1192 » Software that’s easy to keep updated. Download the Mac is a registered trademark of Apple, Inc. latest enhancements from TI’s Web site for free. » Software you can learn to use quickly. Get familiar with the basics in under an hour. No programming required. Take a closer look at TI-Nspire software and get started for free. Visit education.ti.com/us/learnandearn About the Cover: New Orleans Vieux Carré ©2010 Texas Instruments AD10100 (see page 1151) Trim: 8.25" x 10.75" 168 pages on 40 lb Velocity • Spine: 3/16" • Print Cover on 9pt Carolina ,!4%8 ,!4%8 ,!4%8 &DOO IRU DSSOLFDWLRQV $FDGHPLF \HDU 7KH )RXQGDWLRQ 6FLHQFHV 0DWKpPDWLTXHV GH 3DULV LV SOHDVHG WR RIIHU WKH IRO ORZLQJ RSSRUWXQLWLHV WR RXWVWDQGLQJ VFLHQWLVWV DQG H[FHOOHQWVWXGHQWV D7KH)RXQGDWLRQ3UL]H D7KH5HVHDUFK&KDLU D)LIWHHQSRVWGRFWRUDOSRVLWLRQV D3*607HQPDVWHUFRXUVHVFKRODUVKLSV QHZ +RZWRDSSO\ 3URFHGXUHVRIDSSOLFDWLRQVDYDLODEOHDW ZZZVFLHQFHVPDWKVSDULVIU DQGIRU3*60DW ZZZVFLHQFHVPDWKVSDULVIUSJVP )RXQGDWLRQ6FLHQFHV0DWKpPDWLTXHVGH3DULVZZZVFLHQFHVPDWKVSDULVIU ,+3UXH3LHUUHHW0DULH&XULH)3DULV&HGH[ 7HO)D[ )RXQGHUV 6FLHQWLÆFSDUWQHUV 3DUWQHUV AMERICAN MATHEMATICAL SOCIETY Save 50% to 75% on hundreds of titles! Algebra and Algebraic Geometry Notes on Dynamical Systems A Mathematical Gift, III Spectral Theory and Mathematical Jürgen Moser, and Eduard J. Zehnder, The interplay between topology, Physics: A Festschrift in Honor of College Algebra ETH-Zurich, Switzerland functions, geometry, and algebra Barry Simon’s 60th Birthday Henry Burchard Fine Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New Koji Shiga, Yokohama, Japan, and Fritz Gesztesy, Managing Editor, AMS Chelsea Publishing, Volume 354; 1961; Toshikazu Sunada, Tohoku University, University of Missouri, Columbia, MO, 631 pp.; hardcover; ISBN: 978-0-8218-3863-1; York University. List US$72; Sale Price US$25.20; Order code: Courant Lecture Notes, Volume 12; 2005; 256 Sendai, Japan Percy Deift, New York University, CHEL/354.H pp.; softcover; ISBN: 978-0-8218-3577-7; List US$36; Mathematical World, Volume 23; 2005; 129 pp.; Courant Institute, NY, Cherie Galvez, Sale Price US$18.00; Order code: CLN/12 softcover; ISBN: 978-0-8218-3284-4; List US$30; California Institute of Technology, Sale Price US$15.00; Order code: MAWRLD/23 Selected Works of Phillip A. Pasadena, CA, Peter Perry, University of Griffiths with Commentary Spectral Problems Associated with Kentucky, Lexington, KY, and Wilhelm Corner Singularities of Solutions Geometry and Topology Schlag, University of Chicago, IL, Editors Enrico Arbarello, Robert L. Bryant, C. Proceedings of Symposia in Pure to Elliptic Equations Mathematics, Volume 76; Set: 2007; 960 pp.; Herbert Clemens, Maurizio Cornalba, Global Calculus Mark L. Green, Joe Harris, David R. hardcover; ISBN: 978-0-8218-3783-2; List US$169; V. A. Kozlov and V. G. Maz’ya, Sale Price US$42.25; Order code: PSPUM/76 Morrison, and Wilfried Schmid, Editors University of Linköping, Sweden, and S. Ramanan, Chennai Mathematics This book is jointly published by the AMS and J. Rossmann, University of Rostock, Institute, India International Press. Germany Graduate Studies in Mathematics, Volume 65; Number Theory Collected Works, Volume 18; Set: 2003; 2598 pp.; Mathematical Surveys and Monographs, 2005; 316 pp.; hardcover; ISBN: 978-0-8218-3702- 3; List US$58; Sale Price US$20.30; Order code: hardcover; ISBN: 978-0-8218-1066-8; List US$319; Volume 85; 2001; 436 pp.; hardcover; ISBN: 978- Brauer Type Embedding Problems Sale Price US$79.75; Order code: CWORKS/18 0-8218-2727-7; List US$105; Sale Price US$26.25; GSM/65 Order code: SURV/85 Arne Ledet, Texas Tech University, Invariant Theory Variational Problems in Geometry Lubbock, TX Seiki Nishikawa, Mathematical Institute, Titles in this series are co-published with The Fields Mara D. Neusel, Texas Tech University, General Interest Institute for Research in Mathematical Sciences Lubbock, TX Tohoku University, Sendai, Japan (Toronto, Ontario, Canada). Translations of Mathematical Monographs Student Mathematical Library, Volume 36; The Coxeter Legacy Fields Institute Monographs, Volume 21; 2005; 2007; 314 pp.; softcover; ISBN: 978-0-8218-4132- (Iwanami Series in Modern Mathematics), Volume 205; Reflections and Projections 2002; 209 pp.; softcover; ISBN: 978-0-8218-1356- 171 pp.; hardcover; ISBN: 978-0-8218-3726-9; List 7; List US$49; Sale Price US$24.50; Order code: US$55; Sale Price US$19.25; Order code: FIM/21 STML/36 0; List US$49; Sale Price US$24.50; Order code: Chandler Davis and Erich W. Ellers, MMONO/205 University of Toronto, ON, Canada, Automorphic Forms and Analysis Editors Applications A co-publication of the AMS and The Fields Institute Logic and Foundations Interpolation and Sampling in for Research in Mathematical Sciences (Toronto, Peter Sarnak, Princeton University, Ontario, Canada). Computable Functions NJ, and Freydoon Shahidi, Purdue Spaces of Analytic Functions 2006; 320 pp.; hardcover; ISBN: 978-0-8218-3722- University, West Lafayette, IN, Editors A. Shen, Independent University of Kristian Seip, Norwegian University 1; List US$69; Sale Price US$24.15; Order code: Titles in this series are co-published with the COXETER Moscow, Russia, and N. K. Vereshchagin, of Science and Technology, Trondheim, Institute for Advanced Study/Park City Mathematics Moscow State Lomonosov University, Russia Institute. Norway Student Mathematical Library, Volume 19; University Lecture Series, Volume 33; 2004; 139 The Fermat Diary IAS/Park City Mathematics Series, Volume 12; 2003; 166 pp.; softcover; ISBN: 978-0-8218-2732- 2007; 427 pp.; hardcover; ISBN: 978-0-8218-2873- pp.; softcover; ISBN: 978-0-8218-3554-8; List US$30; C. J. Mozzochi, Princeton, NJ 1; List US$32; Sale Price US$16.00; Order code: Sale Price US$15.00; Order code: ULECT/33 1; List US$75; Sale Price US$18.75; Order code: 2000; 196 pp.; hardcover; ISBN: 978-0-8218-2670- STML/19 PCMS/12 6; List US$32; Sale Price US$16.00; Order code: FERMATD Differential Equations Mathematical Physics Probability Ramanujan: Letters and Partial Differential Equations Commentary Strings and Geometry Information Theory and Harold Levine, Stanford University, CA Michael Douglas, Rutgers University, Stochastics for Multiscale Bruce C. Berndt, University of Illinois, Titles in this series are co-published with Piscataway, NJ, Jerome Gauntlett, Urbana, IL, and Robert A. Rankin, Nonlinear Systems International Press, Cambridge, MA. University of London, England, and Mark University of Glasgow, Scotland AMS/IP Studies in Advanced Mathematics, Gross, University of California San Diego, Andrew J. Majda and Rafail V. History of Mathematics, Volume 9; 1995; 347 Volume 6; 1997; 706 pp.; hardcover; ISBN: 978- La Jolla, CA, Editors Abramov, Courant Institute of 0-8218-0775-0; List US$80; Sale Price US$20.00; pp.; softcover; ISBN: 978-0-8218-0470-4; List US$59; Mathematical Sciences, New York Order code: AMSIP/6 Sale Price US$20.65; Order code: HMATH/9.S Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA). University, NY, and Marcus J. Grote, Clay Mathematics Proceedings, Volume 3; 2004; University of Basel, Switzerland 376 pp.; softcover; ISBN: 978-0-8218-3715-3; List Titles in this series are co-published with the Please note: Order online to receive US$72; Sale Price US$25.20; Order code: CMIP/3 Centre de Recherches Mathématiques. CRM Monograph Series, Volume 25 your discount. Discount applies to limited 2005; 133 pp.; hardcover; ISBN: 978-0-8218-3843- 3; List US$41; Sale Price US$20.50; Order code: quantities. Direct sales only. Not available CRMM/25 to bookstores or agents. Go to www.ams.org/bookstore to view the entire list of titles on sale. Notices of the American Mathematical Society October 2010 Communications 1106 1129 1116 Alice Turner Schafer (1915– 2009): Remembrances Georgia Benkart, Bhama Srinivasan, Mary Gray, Ellen Maycock, Linda Rothschild, edited by Anne Leggett 1125 WHAT IS... a Linear Algebraic Group? 1094 1116 Skip Garibaldi 1127 Doceamus: The Doctor Is In Robert Borrelli Features 1132 Meta-Morphism: From The feature articles this month exhibit the dynamic and Graduate Student to diversity of modern mathematics. The article by Chris Byrnes Networked Mathematician considers applications of modern topology to questions of Andrew Schultz physics. The article by Dick Gundy shows how wavelets can 1137 Lovász Receives Kyoto Prize be used to understand probability theory. And the article by Jerry Folland considers questions of communication that will resonate with us all. The interview with Luc Illusie about Commentary Alexander Grothendieck will give us all pause for thought. 1079 Opinion: Agenda for a —Steven G. Krantz Mathematical Renaissance Editor Teodora-Liliana Ra˘dulescu and Vicen¸tiu Ra˘dulescu 1080 Topological Methods for Nonlinear 1129 The Cult of Statistical Oscillations Significance— A Book Review Christopher I. Byrnes Reviewed by Olle Häggström 1094 Tilings, Scaling Functions, and a Markov Process Richard F. Gundy 1106 Reminiscences of Grothendieck and His School Luc Illusie, with Alexander Beilinson, Spencer Bloch, Vladimir Drinfeld, et al. 1121 Speaking with the Natives: Reflections on Mathematical Communication Gerald B. Folland Notices Departments of the American Mathematical Society About the Cover .