ISSN 0002-9920 Notices of the American Mathematical Society ABCD springer.com Highlights in Springer’s eBook of the American Mathematical Society Collection February 2010 Volume 57, Number 2 An Invitation to Cauchy-Riemann NEW 4TH NEW NEW EDITION and Sub-Riemannian Geometries 2010. XIX, 294 p. 25 illus. 4th ed. 2010. VIII, 274 p. 250 2010. XII, 475 p. 79 illus., 76 in 2010. XII, 376 p. 8 illus. (Copernicus) Dustjacket illus., 6 in color. Hardcover color. (Undergraduate Texts in (Problem Books in Mathematics) page 208 ISBN 978-1-84882-538-3 ISBN 978-3-642-00855-9 Mathematics) Hardcover Hardcover $27.50 $49.95 ISBN 978-1-4419-1620-4 ISBN 978-0-387-87861-4 $69.95 $69.95 Mathematics of the Gateway Arch page 220 Model Theory and Complex Geometry 2ND page 230 JOURNAL JOURNAL EDITION NEW 2nd ed. 1993. Corr. 3rd printing 2010. XVIII, 326 p. 49 illus. ISSN 1139-1138 (print version) ISSN 0019-5588 (print version) St. Paul Meeting 2010. XVI, 528 p. (Springer Series (Universitext) Softcover ISSN 1988-2807 (electronic Journal No. 13226 in Computational Mathematics, ISBN 978-0-387-09638-4 version) page 315 Volume 8) Softcover $59.95 Journal No. 13163 ISBN 978-3-642-05163-0 Volume 57, Number 2, Pages 201–328, February 2010 $79.95 Albuquerque Meeting page 318 For access check with your librarian Easy Ways to Order for the Americas Write: Springer Order Department, PO Box 2485, Secaucus, NJ 07096-2485, USA Call: (toll free) 1-800-SPRINGER Fax: 1-201-348-4505 Email: [email protected] or for outside the Americas Write: Springer Customer Service Center GmbH, Haberstrasse 7, 69126 Heidelberg, Germany Call: +49 (0) 6221-345-4301 Fax : +49 (0) 6221-345-4229 Email: [email protected] Prices are subject to change without notice. Differential All prices are net prices. Geometry Issue 014550x (see page 266) Trim: 8.25" x 10.75" 128 pages on 40 lb Velocity • Spine: 1/8" • Print Cover on 9pt Carolina noti-feb10-cov.indd 1 12/28/09 1:34 PM ,!4%8 ,!4%8 ,!4%8 A MERICAN M ATHEMATICAL S OCIETY Mathematical Improving Stents Getting It Together Stents are expandable tubes that are inserted into blocked The collective motion of many groups of animals can be stun- or damaged blood vessels. They offer a practical way to treat ning. Flocks of birds and schools of fish are able to remain coronary artery disease, repairing vessels and keeping them cohesive, find food, and avoid predators without leaders and open so that blood can flow freely. When stents work, they without awareness of all but a few other members in their are a great alternative to radical surgery, but they can dete- groups. Research using vector analysis and statistics has led riorate or become dislodged. Mathematical models of blood to the discovery of simple principles, such as members main- vessels and stents are helping to determine better shapes and taining a minimum distance between neighbors while still materials for the tubes. These models are so accurate that the aligning with them, which help explain shapes such as the one FDA is considering requiring mathematical modeling in the below. Moments design of stents before any further testing is done, to reduce the need for expensive experimentation. A series of over 70 posters that describe the role mathematics plays in science, nature, technol- Photo by Jose Luis Gomez de Francisco. Jose Photo by ogy, and human culture. Some have been trans- Image courtesy of Michel Leconte. The Mathematical Moments program promotes The Mathematical Moments program promotes appreciation and understanding of the role mathematics appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture. plays in science, nature, technology, and human culture. lated into other languages, and some feature MM/72.s www.ams.org /mathmoments MM/68.s www.ams.org/mathmoments podcast interviews with experts in the fi eld. Listen Up! — Podcast Interviews with Experts Diandra L. Leslie-Pelecky, University of Texas at Dallas, on the math- ematics of NASCAR Leslie-Pelecky Golden Ken Golden, University of Utah, on the mathematics of sea ice Kevin Short, University of New Hampshire, on digitizing a wire recording of Woodie Guthrie (and his resulting Grammy© Award) Tim Chartier, Davidson College, on the connections between math- ematics and soccer and more... Short Chartier Mathematical Moments in Other Languages Read translated versions in Chinese, Spanish, French, German, Portuguese, Polish, Japanese, and Russian. 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(SL_HUKLY3\IV[aR`/LIYL^<UP]LYZP[` VM[OL*047(;<)0;(2:\TTLY:JOVVS 1LY\ZHSLT0ZYHLS"1VUH[OHU+9VNH^ZRP (YYHUNLTLU[Z3VJHSZ`Z[LTZHUK:PU ;OL;OLVY`VM[OL;VW <UP]LYZP[`VM*HSPMVYUPH3VZ(UNLSLZ*( N\SHYP[PLZOLSKH[.HSH[HZHYH`<UP]LYZP[` <:( 0Z[HUI\SK\YPUN1\UL;OLYLHKLY^PSS =VS\TL!0U[YVK\J[PVU[V[OL ÄUKH]HYPL[`VMVWLUWYVISLTZPU]VS]PUN 2PULTH[PJZHUK2PUL[PJZVM[OL :;,+ 5+7905;05. HYYHUNLTLU[ZSVJHSZ`Z[LTZHUKZPUN\SHYP ;VW 7:6-;*6=,9 [PLZWYVWVZLKI`[OLSLJ[\YLYZH[[OLLUK 0:)5 VM[OLZJOVVS ?=000 7033<: /(9+*6=,9 690.05(33@7<)30:/,+05;/,:,90,:! :,90,:!796.9,::054(;/,4(;0*: 796.9,::054(;/,4(;0*:=63 0:)5 =63 46+,95)092/f<:,9*3(::0*: 7/(9+*6=,9 0:)5 &$//÷)$; ÷(0$,/RUGHUV#ELUNKDXVHUFRP÷ZZZELUNKDXVHUFRP 7SLHZLTLU[PVUWYVTV[PVU ^OLUVYKLYPUN7YPJLZHYL]HSPKPU[OL(TLYPJHZVUS`HUKHYLZ\IQLJ[[VJOHUNL^P[OV\[UV[PJL -VYWYPJLHUKVYKLYPUNPUMVYTH[PVUV\[ZPKL[OL(TLYPJHZWSLHZLJVU[HJ[)PYROp\ZLY=LYSHN(.I`,THPS!VYKLYZ'IPYROH\ZLYJO [ Notices of the American Mathematical Society February 2010 Communications 244 236 WHAT IS…a Halting Probability? Cristian S. Calude and G. J. Chaitin 248 Simons Foundation Launches US$40-Million Program for Theoretical Research Allyn Jackson 208 208 250 2009 Annual Survey of the Mathematical Sciences (First Report) Ideas of differential geometry have permeated all parts Polly Phipps, James W. of mathematics. Partial differential equations, topology, Maxwell, and Colleen Rose analysis, and many other branches of our subject have taken on a geometric patina. The recent solution of the Poincaré Commentary conjecture used geometry in surprising ways. This issue of the Notices showcases some recent developments in the 205 Opinion: Collaborating geometry of Riemann. on Research with —Steven G. Krantz Mathematicians from Less Editor Developed Countries Melvin Henriksen Features 207 Letters to the Editor 239 What Then? Plato’s 208 An Invitation to Cauchy-Riemann and Ghost: The Modernist Sub-Riemannian Geometries Transformation of John P. D’Angelo and Jeremy T. Tyson Mathematics—A Book Review 220 Mathematics of the Gateway Arch Reviewed by Yuri Manin Robert Osserman 244 Solving Mathematical Problems: A Personal 230 Model Theory and Complex Geometry Perspective—A Book Review Rahim Moosa Reviewed by Loren Larson Notices Departments of the American Mathematical Society About the Cover .