DOCSLIB.ORG

IAMP News Bulletin October 2016

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
IAMP News Bulletin October 2016 IAMP News Bulletin October 2016 International Association of Mathematical Physics Contents International Association of Mathematical Physics News Bulletin, October 2016 Contents Comments from the Editor3 A Walk in Barry Simon's Mathematical Garden4 The Advance of Mathematics, Physics, and Computer Science in Developing Countries 31 Centre for the Mathematics of Quantum Theory (QMATH) at the University of Copenhagen 47 News from the IAMP Executive Committee 49 Contact Coordinates for this Issue 51 Bulletin Editor Editorial Board Evans Harrell Rafael Benguria, Virginie Bonnaillie-No¨el, Yasuyuki Kawahigashi, Manfred Salmhofer, Robert Sims Contacts. http://www.iamp.org and e-mail: [email protected] Cover picture: Barry Simon (photograph courtesy of Bob Paz) The views expressed in this IAMP News Bulletin are those of the authors and do not necessarily represent those of the IAMP Executive Committee, Editor or Editorial Board. Any complete or partial performance or reproduction made without the consent of the author or of his successors in title or assigns shall be unlawful. All reproduction rights are Mhenceforth reserved, and mention of the IAMP News Bulletin is obligatory in theΦ reference. (Art.L.122-4 of the Code of Intellectual Property). ISSN 2304-7348 News Bulletin (International Association of Mathematical Physics) 2 ∩IAMP News Bulletin, October 2016 Comments from the Editor Comments from the Editor As was reported in these pages several months ago, our colleague Barry Simon was awarded the Steele Prize of the American Mathematical Society, for lifetime achievement, and recently his 70th birth year was celebrated with a pair of conferences in Canada. See http://www.fields.utoronto.ca/activities/16-17/modern-physics and http://www.crm.umontreal.ca/2016/Simon16/. We are grateful to the Notices of the American Mathematical Society for permission to reprint two linked articles of reminiscences of Barry throughout his career, which were put together by Fritz Gesztesy. Another feature of this issue is an article on the state of mathematical sciences in the developing world, The Advance of Mathematics, Physics, and Computer Science in Developing Countries, by Wayne Patterson. The author shares perspectives from his extensive experience with scientific programs in developing countries through service at the US National Science Foundation and personal participation in numerous educational and scientific programs. This is the first of a planned series of articles on the spread of mathematical sciences in developing countries. The developing world is an essential topic for anyone concerned with the future of our field. International organizations like the IAMP not only have a philosophical commit- ment to international cooperation, but need to look south out of enlightened self-interest. Consider the remarkable fact that the world-wide adult literacy rate is now at about 85% for the first time in history. The greatest increases in education are taking place in the countries of the Global South, along with the greatest population growth. By the middle of this century the population of Africa, for example, will be substantially larger than either China or India, and with a much younger age distribution. Therefore, in one more generation, a significant fraction of the young researchers entering mathematical physics will very likely arrive from regions of the world that are unfamiliar to many universities and scientific institutions operating today. Knowing about mathematical and scientific activities in these regions and building bridges now will help the IAMP adapt successfully to the coming changes. Evans Harrell, Editor of the IAMP News Bulletin IAMP News Bulletin, October 20163 Fritz Gesztesy From Mathematical Physics to Analysis: A Walk in Barry Simon's Mathematical Garden by Fritz Gesztesy (Baylor University) This article has been reprinted with permission from the original publication in The Notices of the American Mathematical Society 63 (2016) 740-752 and 878-889. 4 IAMP News Bulletin, October 2016 A Walk in Barry Simon's Mathematical Garden Notices of the American Mathematical Society August 2016 FEATURES P * P P 732 740 772 P + P = 2 P Tverberg's Theorem at 50: From Mathematical WHAT IS... Extensions and Physics to Analysis: a Diophantine m-tuple? Counterexamples A Walk in Barry Simon’s by Andrej Dujella by Imre Bárány, Pavle V. M. Blagojevic, Mathematical Garden and Günter M. Ziegler Coordinating Editor Fritz Gesztesy Our August issue features the recent counterexample to the conjectured topological version of Tverberg's 1966 theorem and 2016 Steele Prize winner Barry Simon on the occasion of his 70th birthday conference this month. —Frank Morgan, Editor-in-Chief ALSO IN THIS ISSUE THE GRADUATE STUDENT SECTION Report on the 2014–2015 New Doctoral Recipients 754 Helen Moore Interview 768 William Yslas Vélez, Thomas H. Barr, and Colleen A. Rose Alexander Diaz-Lopez AMS Executive Director Donald E. McClure Retires 777 Allyn Jackson FROM THE SECRETARY'S OFFICE Chinese Mathematics and ICCM 780 Voting Information for 2016 AMS Election 775 Lizhen Ji Baa Hózhó Math: Math Circles for Navajo Students and Teachers 784 Dave Auckly, Bob Klein, Amanda Serenevy, and Tatiana Shubin Doctoral Degrees Conferred 790 The background figures on the cover show reflections 2014–2015 in the Poincaré Disk (left) and a spiraling line compac- tification that adds a circle at infinity (right) © Mihai The Mathematics of Love 821 Stoiciu, from Barry Simon's 5-volume set A Compre- Reviewed by Marc Colyvan hensive Course in Analysis. bookstore.ams.org/simon-set IAMP News Bulletin, October 20165 Fritz Gesztesy 1., 3'#,3(!+ '82(!2 3. -+82(2đ +* (- 118 (,.-ġ2 3'#,3(!+ 1"#- &EJUPSůT /PUF 'SJU[ (FT[UFTZ LJOEMZ BDDFQUFE PVS JOWJUBUJPO UP QVU UPHFUIFS UIJT GFBUVSF JO IPOPS PG #BSSZ 4JNPO PO UIF PDDBTJPO PG 4JNPOůT ".4 -FSPZ 1 4UFFMF 1SJ[F GPS -JGFUJNF "DIJFWFNFOU BOE IJT UI CJSUIEBZ DPOGFSFODF UIJT "VHVTU Ŭ4FQUFNCFS 'SJU[ (FT[UFTZ IJT JT B DPMMFDUJPO PG DPOUSJCVUJPOT CZ DPMMBCP SBUPST QPTUEPDT BOE TUVEFOUT PG #BSSZ 4JNPO PG UIF $BMJGPSOJB *OTUJUVUF PG 5FDIOPMPHZ PO UIF PDDBTJPO PG 4JNPOʍT SFDFJWJOH UIF ".4 -FSPZ 1 4UFFMF 1SJ[F GPS -JGFUJNF "DIJFWFNFOU 5IF5 DJUBUJPO GPS UIF BXBSE NFOUJPOT IJT USFNFOEPVT JN QBDU PO UIF FEVDBUJPO BOE SFTFBSDI PG B XIPMF HFOFSBUJPO PG NBUIFNBUJDBM TDJFOUJTUT BOE XF XJMM VOEFSTDPSF UIJT CZ EFNPOTUSBUJOH IJT QFOFUSBUJOH JOʲVFODF PO UPQJDT SBOHJOH GSPN RVBOUVN ʱFME UIFPSZ TUBUJTUJDBM NFDIBOJDT UIF HFOFSBM UIFPSZ PG 4DIS¶EJOHFS PQFSBUPST TQFDUSBM BOE JOWFSTF TQFDUSBM UIFPSZ UP PSUIPHPOBM QPMZOPNJBMT #VU XF TIPVME TUBSU BU UIF CFHJOOJOH #BSSZ XBT CPSO UP QBSFOUT .JOOJF BOE )Z 4JNPO JO BOE UPHFUIFS XJUI IJT PMEFS CSPUIFS 3JDL HSFX VQ JO #SPPLMZO /FX :PSL 5IFSF IF BUUFOEFE +BNFT .BEJTPO )JHI 4DIPPM PCUBJOJOH #BSSZ 4JNPO XJUI IJT NPUIFS BOE CSPUIFS 3JDL MFGU B QFSGFDU TDPSF PO UIF .""ʍT "NFSJDBO )JHI 4DIPPM BOE XJUI IJT GBUIFS SJHIU DB .BUIFNBUJDT &YBNJOBUPO JO BOE UIVT CFDPNJOH UIF TVCKFDU PG BO BSUJDMF JO UIF /FX :PSL 5JNFT BU UIF UFOEFS BHF PG TJYUFFO 6OEFS UIF JOʲVFODF PG 4BN .BSBOU[ BO JOTQJSJOH QIZTJDT UFBDIFS JO IJHI TDIPPM IF BQQMJFE UP #BSSZ 4JNPO DPNQMFUFE IJT EPDUPSBUF JO QIZTJDT BU )BSWBSE BOE XBT BENJUUFE 8IJMF BU )BSWBSE IF XBT B UPQ 1SJODFUPO VOEFS 8JHIUNBOʍT TVQFSWJTJPO JO 5IF ʱ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ʱFME UIFPSZ 'SJU[ (FT[UFTZ JT .BIBMB BOE 3PTF )PVDIJOT 1SPGFTTPS PG .BUIF TUBUJTUJDBM NFDIBOJDT BOE OPOSFMBUJWJTUJD RVBOUVN NF NBUJDT BU UIF 6OJWFSTJUZ PG .JTTPVSJ $PMVNCJB )JT FNBJM BEESFTT JT HFT[UFTZG!NJTTPVSJFEV 4JODF "VHVTU IF JT +FBO BOE DIBOJDT #BSSZ KPJOFE $BMUFDI JO IPMEJOH UIF QPTJUJPO 3BMQI 4UPSN $IBJS PG .BUIFNBUJDT BU #BZMPS 6OJWFSTJUZ )JT FNBJM PG *#. 1SPGFTTPS PG .BUIFNBUJDT BOE 5IFPSFUJDBM 1IZTJDT BEESFTT UIFSF JT 'SJU[@(FT[UFTZ!CBZMPSFEV TJODF "U $BMUFDI #BSSZʍT JOUFSFTUT GVSUIFS CSPBE 'PS QFSNJTTJPO UP SFQSJOU UIJT BSUJDMF QMFBTF DPOUBDU FOFE JOUP BSFBT TVDI BT SBOEPN BOE FSHPEJD 4DIS¶EJOHFS SFQSJOUQFSNJTTJPO!BNTPSH PQFSBUPST FYPUJD TQFDUSB JOWFSTF TQFDUSBM UIFPSZ BOE UIF %0* IUUQEYEPJPSHOPUJ BOBMZUJD UIFPSZ PG PSUIPHPOBM QPMZOPNJBMT /ƪƯƤƞƠƮ ƪơ ƯƣƠ ".4 7ƪƧưƨƠ /ưƨƝƠƭ 6 IAMP News Bulletin, October 2016 A Walk in Barry Simon's Mathematical Garden B QSPPG PG DPOUJOVPVT TZNNFUSZ CSFBLJOH JO ŀ DMBTTJDBM BOE RVBOUVN TUBUJTUJDBM NPEFMT 5IPNBTʊ'FSNJ UIFPSZ TFNJDMBTTJDBM CPVOET OPO ŀ 8FZM BTZNQUPUJDT BTZNQUPUJD QFSUVSCBUJPO UIFPSZ PG FJHFOWBMVFT ŀ #PSFM BOE 1BE© TVNNBCJMJUZ ;FFNBO FʰFDU BOIBS NPOJD PTDJMMBUPST JOTUBOUPO UVOOFMJOH #JSNBOʊ 4DIXJOHFS QSJODJQMF DPVQMJOH DPOTUBOU UISFTI PMET HFOFSBM UIFPSZ PG 4DIS¶EJOHFS PQFSBUPST FTTFO ŀ UJBM TFMGBEKPJOUOFTT QPJOUXJTF CPVOET PO FJHFO GVODUJPOT QBUI JOUFHSBM UFDIOJRVFT BCTFODF PG TJOHVMBS DPOUJOVPVT TQFDUSVN JO CPEZ TZUFNT #FSSZʍT QIBTF BOE IPMPOPNZ IPNPUPQJDւ JOUFSQSF ŀ UBUJPO PG UIF 5IPVMFTT JOUFHFST BOE UPQPMPHJDBM TUSVDUVSF JO UIF JOUFHFS RVBOUVN )BMM FʰFDU SBOEPN BOE BMNPTU QFSJPEJD 4DIS¶EJOHFS BOE ŀ +BDPCJ PQFSBUPST FYPUJD TQFDUSBM QIFOPNFOB $BO
Load more

Recommended publications
  • 286365111.Pdf
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Caltech Authors PROOF OF THE STRONG SCOTT CONJECTURE FOR CHANDRASEKHAR ATOMS RUPERT L. FRANK, KONSTANTIN MERZ, HEINZ SIEDENTOP, AND BARRY SIMON Dedicated to Yakov Sinai on the occasion of his 85th birthday. Abstract. We consider a large neutral atom of atomic number Z, taking rel- ativistic effects into account by assuming the dispersion relation pc2p2 + c4. We study the behavior of the one-particle ground state density on the length scale Z−1 in the limit Z; c ! 1 keeping Z=c fixed and find that the spher- ically averaged density as well as all individual angular momentum densities separately converge to the relativistic hydrogenic ones. This proves the gen- eralization of the strong Scott conjecture for relativistic atoms and shows, in particular, that relativistic effects occur close to the nucleus. Along the way we prove upper bounds on the relativistic hydrogenic density. 1. Introduction 1.1. Some results on large Z-atoms. The asymptotic behavior of the ground state energy and the ground state density of atoms with large atomic number Z have been studied in detail in non-relativistic quantum mechanics. Soon after the advent of quantum mechanics it became clear that the non- relativistic quantum multi-particle problem is not analytically solvable and of in- creasing challenge with large particle number. This problem was addressed by Thomas [51] and Fermi [11, 12] by developing what was called the statistical model of the atom. The model is described by the so-called Thomas{Fermi functional (Lenz [28]) Z ZZ TF 3 5=3 Z 1 ρ(x)ρ(y) (1) EZ (ρ) := 10 γTFρ(x) − ρ(x) dx + dx dy ; 3 jxj 2 3 3 jx − yj R R ×R | {z } =:D[ρ] 2 2=3 where γTF = (6π =q) is a positive constant depending on the number q of spin states per electron, i.e., physically 2.
    [Show full text]
  • On a Paley-Wiener Theorem for the Zs-Akns Scattering Transform
    University of Kentucky UKnowledge Theses and Dissertations--Mathematics Mathematics 2013 ON A PALEY-WIENER THEOREM FOR THE ZS-AKNS SCATTERING TRANSFORM Ryan D. Walker University of Kentucky, [email protected] Right click to open a feedback form in a new tab to let us know how this document benefits ou.y Recommended Citation Walker, Ryan D., "ON A PALEY-WIENER THEOREM FOR THE ZS-AKNS SCATTERING TRANSFORM" (2013). Theses and Dissertations--Mathematics. 9. https://uknowledge.uky.edu/math_etds/9 This Doctoral Dissertation is brought to you for free and open access by the Mathematics at UKnowledge. It has been accepted for inclusion in Theses and Dissertations--Mathematics by an authorized administrator of UKnowledge. For more information, please contact [email protected]. STUDENT AGREEMENT: I represent that my thesis or dissertation and abstract are my original work. Proper attribution has been given to all outside sources. I understand that I am solely responsible for obtaining any needed copyright permissions. I have obtained and attached hereto needed written permission statements(s) from the owner(s) of each third-party copyrighted matter to be included in my work, allowing electronic distribution (if such use is not permitted by the fair use doctrine). I hereby grant to The University of Kentucky and its agents the non-exclusive license to archive and make accessible my work in whole or in part in all forms of media, now or hereafter known. I agree that the document mentioned above may be made available immediately for worldwide access unless a preapproved embargo applies. I retain all other ownership rights to the copyright of my work.
    [Show full text]
  • On the Evolution of Scattering Data Under Perturbations of the Toda Lattice
    ON THE EVOLUTION OF SCATTERING DATA UNDER PERTURBATIONS OF THE TODA LATTICE DENIZ BILMAN AND IRINA NENCIU Abstract. We present the results of an analytical and numerical study of the long-time behavior for certain Fermi-Pasta-Ulam (FPU) lattices viewed as perturbations of the completely integrable Toda lattice. Our main tools are the direct and inverse scattering transforms for doubly-infinite Jacobi matrices, which are well-known to linearize the Toda flow. We focus in particular on the evolution of the associated scattering data under the perturbed vs. the unperturbed equations. We find that the eigenvalues present initially in the scattering data converge to new, slightly perturbed eigenvalues under the perturbed dynamics of the lattice equation. To these eigenvalues correspond solitary waves that emerge from the solitons in the initial data. We also find that new eigenvalues emerge from the continuous spectrum as the lattice system is let to evolve under the perturbed dynamics. 1. Introduction The purpose of this work is to numerically investigate the long time behavior of solutions to certain perturbations of the completely integrable Toda lattice. In its wider context, this prob- lem lies within a set of fundamental questions concerning the qualitative features of solutions to nonlinear Hamiltonian partial differential or difference equations (PDEs or P∆Es, respectively). It is well known that in these types of equations several different phenomena can appear over long times, among them blow-up, scattering to the free evolution, or the emergence of stable nonlinear structures, such as solitary waves and breather solutions. A detailed description of any such phe- nomenon often depends on the precise structure of the equation in question.
    [Show full text]
  • November 10, 2019 CURRICULUM VITAE Barry Simon IBM Professor
    November 10, 2019 CURRICULUM VITAE Barry Simon IBM Professor of Mathematics and Theoretical Physics California Institute of Technology Pasadena, CA 91125 DATE OF BIRTH: April 16, 1946 EDUCATION A.B., summa cum laude, Harvard College, 1966 Ph.D. (Physics), Princeton University, 1970 POSITIONS AND TEACHING EXPERIENCE ◦ 1969/70 { Instructor, Department of Mathematics, Princeton ◦ 1970/72 { Assistant Professor, Departments of Mathematics and Physics, Princeton ◦ 1972/76 { Associate Professor, Departments of Mathematics and Physics, Princeton ◦ 1972/73 { On leave as Visiting Professor at IHES, Bures-sur-Yvette, France and the ETH, Zurich, Switzerland ◦ 1976/81 { Professor, Departments of Mathematics and Physics, Prince- ton ◦ 1976/77 { On leave as Visiting Professor at Department of Physics, Yeshiva University, NYC ◦ 1980/81 { On leave as a Sherman Fairchild Distinguished Visiting Scholar at California Institute of Technology ◦ 1981/ { Professor of Mathematics and Theoretical Physics, California Institute of Technology ◦ 1984/ { IBM Professor of Mathematics and Theoretical Physics, Cali- fornia Institute of Technology ◦ 2016/ { IBM Professor of Mathematics and Theoretical Physics, Emer- itus, California Institute of Technology HONORARY DEGREES ◦ D.Sc.h.c., Technion-Israel Institute of Technology, 1999 ◦ Honorary Fellow, University of Wales Swansea, 2006 1 ◦ D.h.c., Ludwig-Maximilians-Universit¨atM¨unchen, 2014 HONORS ◦ 1965 Putnam Competition Winner (top five group) ◦ Sloan Foundation Fellow, 1972{76 ◦ Medal of International Academy of Atomic and Molecular Science, 1981 ◦ Fellow, American Physical Society, 1981 ◦ Stampacchia Prize, 1982 ◦ Guggenheim Fellowship, 1988{1989 ◦ Corresponding Member, Austrian Academy of Sciences, 1990 ◦ Fellow, American Academy of Arts and Sciences, 2005 ◦ Poincar´ePrize, 2012 ◦ Fellow, American Math. Society, 2013 ◦ Simons Foundation Fellowship in Mathematics, 2013 ◦ Jew in the City Orthodox Allstars, 2014 (previous honoraries include Joe Lieberman and Jack Lew) ◦ Bolyai Prize of the Hungarian Academy of Sciences, 2015 ◦ American Math.
    [Show full text]
  • Real Analysis a Comprehensive Course in Analysis, Part 1
    Real Analysis A Comprehensive Course in Analysis, Part 1 Barry Simon Real Analysis A Comprehensive Course in Analysis, Part 1 http://dx.doi.org/10.1090/simon/001 Real Analysis A Comprehensive Course in Analysis, Part 1 Barry Simon Providence, Rhode Island 2010 Mathematics Subject Classification. Primary 26-01, 28-01, 42-01, 46-01; Secondary 33-01, 35-01, 41-01, 52-01, 54-01, 60-01. For additional information and updates on this book, visit www.ams.org/bookpages/simon Library of Congress Cataloging-in-Publication Data Simon, Barry, 1946– Real analysis / Barry Simon. pages cm. — (A comprehensive course in analysis ; part 1) Includes bibliographical references and indexes. ISBN 978-1-4704-1099-5 (alk. paper) 1. Mathematical analysis—Textbooks. I. Title. QA300.S53 2015 515.8—dc23 2014047381 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy select pages for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Permissions to reuse portions of AMS publication content are handled by Copyright Clearance Center’s RightsLink service. For more information, please visit: http://www.ams.org/rightslink. Send requests for translation rights and licensed reprints to [email protected]. Excluded from these provisions is material for which the author holds copyright.
    [Show full text]
  • Meetings of the MAA Ken Ross and Jim Tattersall
    Meetings of the MAA Ken Ross and Jim Tattersall MEETINGS 1915-1928 “A Call for a Meeting to Organize a New National Mathematical Association” was DisseminateD to subscribers of the American Mathematical Monthly and other interesteD parties. A subsequent petition to the BoarD of EDitors of the Monthly containeD the names of 446 proponents of forming the association. The first meeting of the Association consisteD of organizational Discussions helD on December 30 and December 31, 1915, on the Ohio State University campus. 104 future members attendeD. A three-hour meeting of the “committee of the whole” on December 30 consiDereD tentative Drafts of the MAA constitution which was aDopteD the morning of December 31, with Details left to a committee. The constitution was publisheD in the January 1916 issue of The American Mathematical Monthly, official journal of The Mathematical Association of America. Following the business meeting, L. C. Karpinski gave an hour aDDress on “The Story of Algebra.” The Charter membership included 52 institutions and 1045 inDiviDuals, incluDing six members from China, two from EnglanD, anD one each from InDia, Italy, South Africa, anD Turkey. Except for the very first summer meeting in September 1916, at the Massachusetts Institute of Technology (M.I.T.) in CambriDge, Massachusetts, all national summer anD winter meetings discussed in this article were helD jointly with the AMS anD many were joint with the AAAS (American Association for the Advancement of Science) as well. That year the school haD been relocateD from the Back Bay area of Boston to a mile-long strip along the CambriDge siDe of the Charles River.
    [Show full text]
  • Statistical Theory of the Atom in Momentum Space
    STATISTICAL THEORY OF THE ATOM IN MOMENTUM SPACE dissertation an der fakultat¨ fur¨ mathematik, informatik und statistik der ludwig-maximilians-universitat¨ munchen¨ eingereicht von Verena von Conta am 19.11.2014 1. Gutachter: Prof. Dr. Heinz Siedentop 2. Gutachter: Prof. Dr. Simone Warzel Tag der Disputation: 13.04.2015 Zusammenfassung Im Jahre 1992 fuhrte¨ Englert [3] ein Impuls-Energie-Funktional fur¨ Atome ein und er¨orterte seinen Zusammenhang mit dem Thomas- Fermi-Funktional (Lenz [8]). Wir integrieren dieses Modell in eine ma- thematische Umgebung. Unter unseren Resultaten findet sich ein Be- weis fur¨ die Existenz und Eindeutigkeit einer minimierenden Impuls- dichte fur¨ dieses Impuls-Energie-Funktional; des Weiteren untersuchen wir einige Eigenschaften des Minimierers, darunter auch den Zusam- menhang mit der Euler-Gleichung. Wir verknupfen¨ die Minimierer des Thomas-Fermi-Funktionals mit dem Impuls-Energie-Funktional von Englert durch explizite Transfor- mationen. Wie sich herausstellt, k¨onnen auf diese Weise bekannte Er- gebnisse aus dem Thomas-Fermi-Modell direkt auf das von uns be- trachtete Modell ubertragen¨ werden. Wir erhalten sogar die Aquiva-¨ lenz der beiden Funktionale bezuglich¨ ihrer Minima. Abschließend betrachten wir impulsabh¨angige St¨orungen. Insbeson- dere zeigen wir, dass die atomare Impulsdichte fur¨ große Kernladung in einem bestimmten Sinne gegen den Minimierer des Impuls-Energie- Funktionals konvergiert. Die vorliegende Arbeit basiert auf Zusammenarbeit mit Prof. Dr. Heinz Siedentop. Wesentliche Inhalte werden ebenfalls in einer ge- meinsamen Publikation [27] erscheinen. Abstract In 1992, Englert [3] found a momentum energy functional for atoms and discussed the relation to the Thomas-Fermi functional (Lenz [8]). We place this model in a mathematical setting.
    [Show full text]
  • AMS Bookstore
    American Mathematical Society Distribution Center 35 Monticello Place, Pawtucket, RI 02861 USA AMERICAN MATHEMATICAL SOCIETY A Comprehensive Course in Analysis Part 1: Real Analysis Barry Simon, California Institute of Technology, Pasadena, CA Part 2A: Basic Complex Analysis Part 2B: Advanced Complex Analysis A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level anal- Part 3: Harmonic Analysis ysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and Part 4: Operator Theory provide important historical background. Depth and breadth of Set: 2015; 3259 pages; Hardcover; ISBN: 978-1-4704-1098-8; List US$350; exposition make this set a valuable reference source for almost all AMS members US$280; Order code SIMON-SET areas of classical analysis. For more information go to www.ams.org/simon-set Hear from the author himself at www.facebook.com/simon.analysis. Also of interest: Analysis Functional Analysis An Epsilon of Room, I: Second Edition An Introduction Real Analysis Elliott H. Lieb, Princeton University, Yuli Eidelman and Vitali Milman, pages from year three of a mathemat- NJ, and Michael Loss, Georgia Institute Tel Aviv University, Israel, and Antonis ical blog of Technology, Atlanta, GA Tsolomitis, University of the Aegean, Terence Tao, University of California, Samos, Greece Los Angeles, CA Graduate Studies in Mathematics, Volume 14; 2001; 348 pages; Hardcover; ISBN: Graduate Studies in Mathematics, Graduate Studies in Mathematics, 978-0-8218-2783-3; List US$48; AMS members Volume 66; 2004; 322 pages; Hardcover; ISBN: Volume 117; 2010; 349 pages; Hardcover; ISBN: US$38.40; Order code GSM/14.R 978-0-8218-3646-0; List US$65; AMS members 978-0-8218-5278-1; List US$66; AMS members US$52; Order code GSM/66 US$52.80; Order code GSM/117 Or Order by Phone: facebook.com/amermathsoc (800)321-4267 (U.S.
    [Show full text]
  • History of RSB Interview: Francesco Guerra January 26, 2021, 8:30Am-10:30Pm (EST)
    History of RSB Interview: Francesco Guerra January 26, 2021, 8:30am-10:30pm (EST). Final revision: May 10, 2021 Interviewers: Patrick Charbonneau, Duke University, [email protected] Francesco Zamponi, ENS-Paris Location: Over Zoom, from Prof. Guerra’s second home in Genova, Italy. How to cite: P. Charbonneau, History of RSB Interview: Francesco Guerra, transcript of an oral history conducted 2021 by Patrick Charbonneau and Francesco Zamponi, History of RSB Project, CAPHÉS, École normale supérieure, Paris, 2021, 27 p. https://doi.org/10.34847/nkl.05bd6npc PC: Hello, Professor Guerra. Thank you very much for joining us. As we've dis- cussed, today we will be mostly discussing the history of replica symmetry breaking in a broad sense. Before we get there, however, we wanted to ask you a few questions about your background and interests. In particular, could you tell us what led you to be interested in physics and to pursue a Laurea degree in theoretical physics? FG: Like many people in Italy, in the first two years of university I was enrolled in engineering, like Ettore Majorana1 for example. Then I found that I was more interested in basic scientific questions, so I decided to shift to phys- ics. It was the start in Naples at the time—it was ‘62—of new, big enter- prises in physics. In Naples, there was the old institute of physics and they were involved mostly in classical physics, spectroscopy, solid state physics, and so on. Then, in the middle of the ‘50s, modern physics underwent an impressive development. My big boss at the time was Eduardo Caianiello2.
    [Show full text]
  • Barry Simon and the János Bolyai International Mathematical Prize
    Barry Simon and the J´anosBolyai International Mathematical Prize Vilmos Totik∗ February 26, 2016 1 Introduction The recipient of the 2015 J´anosBolyai International Mathematical Prize was Barry Simon (IBM Professor California Institute of Technology). The prize is given every 5 years by the Hungarian Academy of Sciences on the recommen- dation of a 10 member international committee (this is the only international prize of the Academy). It was established in 1902 for the 100th birth anniver- sary of the great Hungarian mathematician J´anosBolyai, one of the founders of non-Euclidean geometry, and the first two awardees were Henry Poincar´e(1905) and David Hilbert (1910). Then came World War I and the prize was not given until 2000, when the Academy renewed it. It is commonly accepted that, since there is no Nobel prize in mathematics, part of the original intention was to have a prestigious substitute that honors high quality mathematical work. In the renewed form the prize is given for monographs of high impact written in the preceding 10-15 years. In 2000 Saharon Shelah was the recipient for his book \Cardinal Arithmetic", in 2005 Mikhail Gromov got it for the monograph \Metric structures for Riemannian and non-Riemannian spaces", and the 2010 awardee was Yurii Manin for this work \Frobenius manifolds, quantum coho- mology, and moduli spaces". Barry Simon received the Bolyai Prize for his monumental two-volume trea- tise \Orthogonal Polynomials on the Unit Circle" published by the American Mathematical Society in the Colloquium Publications series in 2005. Simon does not need much introduction: he is one of the most cited mathematicians; the author of 21 monographs that has had profound influence on various fields of physics, mathematical physics and mathematics; among others he is the recipi- ent of the Poincar´ePrize (2012), the Leroy P.
    [Show full text]
  • Publications My Most Important Works Are [7], [11], [20], [27], [29], [30]
    Publications My most important works are [7], [11], [20], [27], [29], [30]. My personal favorite is [29], for which a preliminary version is available from my home page. Close runners up are [10], [18], and [31]. Published: 32 Analyticity of extremizers to the Airy-Strichartz inequality, with Shuanglin Shao. Bull. Lond. Math. Soc. 44 (2012), no. 2, 336–352. 31 On non-local variational problems with lack of compactness related to non-linear optics, with Young-Ran Lee. J. Nonlinear Sci. 22 (2012), no. 1, 1–38. 30 Super-exponential decay of diffraction managed solitons, with Young-Ran Lee. Comm. Math. Phys. 309 (2012), no. 1, 1–21. 29 Exponential decay of dispersion management solitons, with Burak Erdogan and Young-Ran Lee. Math. Res. Lett. 18 (2011), no. 1, 11–24. 28 Heat-flow monotonicity of Strichartz norms, with Jonathan Bennett, Neal Bez, and Anthony Carbery. Anal. PDE 2 (2009), no. 2, 147–158. 27 Decay estimates and smoothness for solutions of the dispersion managed non-linear Schr¨odinger equation, with Young-Ran Lee. Comm. Math. Phys. 286 (2009), no. 3, 851–873. DOI 10.1007/s00220-008-0612-4. 26 A unified theoretical framework for fluctuating-charge models in atom-space and in bond- space, with Jiahao Chen and Todd Martinez, 44pp. J. Chem. Phys. 129, 214113 (2008); DOI:10.1063/1.3021400 25 Improved Hardy-Sobolev inequalities, with Alex Balinsky, Des Evans, and Roger Lewis. Ba- nach J. Math. Anal. 2 (2008), no. 2, 94–106. 24 A short introduction to Anderson localization, to appear in the proceedings of the LMS Meet- ing on Analysis and Stochastics of Growth Processes, Bath, September 2006, 25 pp.
    [Show full text]
  • Relativistic Strong Scott Conjecture: a Short Proof
    RELATIVISTIC STRONG SCOTT CONJECTURE: A SHORT PROOF RUPERT L. FRANK, KONSTANTIN MERZ, AND HEINZ SIEDENTOP Abstract. We consider heavy neutral atoms of atomic number Z modeled with kinetic energy (c2p2 + c4)1/2 − c2 used already by Chandrasekhar. We study the behavior of the one-particle ground state density on the length scale Z−1 in the limit Z,c →∞ keeping Z/c fixed. We give a short proof of a recent result by the authors and Barry Simon showing the convergence of the density to the relativistic hydrogenic density on this scale. 1. Introduction A simple description exhibiting some qualitative features of atoms of large atomic number Z with N electrons and with q spin states each is offered by the Chan- drasekhar operator N Z 1 N (1) c2∆ + c4 c2 + in L2(R3 : Cq) − ν − − x x x ν=1 ν 1 ν µ ν=1 X p | | ≤ν<µX≤N | − | ^ where c denotes the velocity of light. It is defined as the Friedrichs extension of N ∞ R3 Cq the corresponding quadratic form with form domain ν=1 C0 ( : ). By Kato’s inequality [7, Chapter 5, Equation (5.33)], it follows that the form is bounded from below if and only if Z/c 2/π (see also Herbst [5, TheoremV 2.5] and Weder [14]). N ≤ 1/2 R3N Cq N 2 R3 Cq For Z/c < 2/π its form domain is H ( : ) ν=1 L ( : ). Since there is no interaction involving the electron’s spin present,∩ we set q = 1 for notational simplicity. Moreover, we are restricting ourselves toV neutral atoms N = Z and fix γ = Z/c (0, 2/π).
    [Show full text]