Program of the Sessions San Diego, California, January 10–13, 2018
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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. -
The William Lowell Putnam Mathematical Competition 1985–2000 Problems, Solutions, and Commentary
The William Lowell Putnam Mathematical Competition 1985–2000 Problems, Solutions, and Commentary i Reproduction. The work may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents. In any reproduction, the original publication by the Publisher must be credited in the following manner: “First published in The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commen- tary, c 2002 by the Mathematical Association of America,” and the copyright notice in proper form must be placed on all copies. Ravi Vakil’s photo on p. 337 is courtesy of Gabrielle Vogel. c 2002 by The Mathematical Association of America (Incorporated) Library of Congress Catalog Card Number 2002107972 ISBN 0-88385-807-X Printed in the United States of America Current Printing (last digit): 10987654321 ii The William Lowell Putnam Mathematical Competition 1985–2000 Problems, Solutions, and Commentary Kiran S. Kedlaya University of California, Berkeley Bjorn Poonen University of California, Berkeley Ravi Vakil Stanford University Published and distributed by The Mathematical Association of America iii MAA PROBLEM BOOKS SERIES Problem Books is a series of the Mathematical Association of America consisting of collections of problems and solutions from annual mathematical competitions; compilations of problems (including unsolved problems) specific to particular branches of mathematics; books on the art and practice of problem solving, etc. Committee on Publications Gerald Alexanderson, Chair Roger Nelsen Editor Irl Bivens Clayton Dodge Richard Gibbs George Gilbert Art Grainger Gerald Heuer Elgin Johnston Kiran Kedlaya Loren Larson Margaret Robinson The Inquisitive Problem Solver, Paul Vaderlind, Richard K. -
Tōhoku Rick Jardine
INFERENCE / Vol. 1, No. 3 Tōhoku Rick Jardine he publication of Alexander Grothendieck’s learning led to great advances: the axiomatic description paper, “Sur quelques points d’algèbre homo- of homology theory, the theory of adjoint functors, and, of logique” (Some Aspects of Homological Algebra), course, the concepts introduced in Tōhoku.5 Tin the 1957 number of the Tōhoku Mathematical Journal, This great paper has elicited much by way of commen- was a turning point in homological algebra, algebraic tary, but Grothendieck’s motivations in writing it remain topology and algebraic geometry.1 The paper introduced obscure. In a letter to Serre, he wrote that he was making a ideas that are now fundamental; its language has with- systematic review of his thoughts on homological algebra.6 stood the test of time. It is still widely read today for the He did not say why, but the context suggests that he was clarity of its ideas and proofs. Mathematicians refer to it thinking about sheaf cohomology. He may have been think- simply as the Tōhoku paper. ing as he did, because he could. This is how many research One word is almost always enough—Tōhoku. projects in mathematics begin. The radical change in Gro- Grothendieck’s doctoral thesis was, by way of contrast, thendieck’s interests was best explained by Colin McLarty, on functional analysis.2 The thesis contained important who suggested that in 1953 or so, Serre inveigled Gro- results on the tensor products of topological vector spaces, thendieck into working on the Weil conjectures.7 The Weil and introduced mathematicians to the theory of nuclear conjectures were certainly well known within the Paris spaces. -
Of the American Mathematical Society August 2017 Volume 64, Number 7
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society August 2017 Volume 64, Number 7 The Mathematics of Gravitational Waves: A Two-Part Feature page 684 The Travel Ban: Affected Mathematicians Tell Their Stories page 678 The Global Math Project: Uplifting Mathematics for All page 712 2015–2016 Doctoral Degrees Conferred page 727 Gravitational waves are produced by black holes spiraling inward (see page 674). American Mathematical Society LEARNING ® MEDIA MATHSCINET ONLINE RESOURCES MATHEMATICS WASHINGTON, DC CONFERENCES MATHEMATICAL INCLUSION REVIEWS STUDENTS MENTORING PROFESSION GRAD PUBLISHING STUDENTS OUTREACH TOOLS EMPLOYMENT MATH VISUALIZATIONS EXCLUSION TEACHING CAREERS MATH STEM ART REVIEWS MEETINGS FUNDING WORKSHOPS BOOKS EDUCATION MATH ADVOCACY NETWORKING DIVERSITY blogs.ams.org Notices of the American Mathematical Society August 2017 FEATURED 684684 718 26 678 Gravitational Waves The Graduate Student The Travel Ban: Affected Introduction Section Mathematicians Tell Their by Christina Sormani Karen E. Smith Interview Stories How the Green Light was Given for by Laure Flapan Gravitational Wave Research by Alexander Diaz-Lopez, Allyn by C. Denson Hill and Paweł Nurowski WHAT IS...a CR Submanifold? Jackson, and Stephen Kennedy by Phillip S. Harrington and Andrew Gravitational Waves and Their Raich Mathematics by Lydia Bieri, David Garfinkle, and Nicolás Yunes This season of the Perseid meteor shower August 12 and the third sighting in June make our cover feature on the discovery of gravitational waves -
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 -
Mathematical Association of America Ohio Section
Program of Activities For the 90 th Annual Meeting of the Mathematical Association of America Ohio Section Spring 2006 The University of Akron Akron, Ohio March 31-April 1, 2006 MAA Ohio Section Program Friday, March 31, 2006 8:00—Noon NExT Workshop College of Arts and Sciences Building (CAS) Room 134 Noon—4:30 Registration Student Union, Second Floor, Theatre Area Book exhibits Student Union, Second Floor, Atrium Noon—1:20 Student problem-solving team competition CAS 107 12:15—1:15 Committee Meetings CONCUR Student Union, 308 CONSACT Student Union, 310 CONSTUM Student Union, 312 CONTEAL Student Union, 314 Program Committee Student Union, 316 1:30—1:45 Welcome and Announcements Student Union Theatre 1:45—2:45 Invited address: Student Union Theatre “Going Up and Down” Georgia Benkart, University of Wisconsin – Madison 2:45—3:10 Break & refreshments Lobby Area, Student Union 3:10—4:05 Retiring President’s address: Student Union Theatre “Some Thoughts on Rings and Things” Dwight Olson, John Carroll University 4:20—6:15 Contributed p aper sessions College of Arts and Sciences Bldg (CAS) 4:20—6:15 Special session on Applied Mathematics CAS 4:20—6:15 Executive Committee Meeting CAS 124 Conference Room 6:15—6:45 Social Time Martin University Center (Fir Street) 6:45—8:00 Banquet Martin University Center (Fir Street) 6:15—8:00 Student Pizza Party CAS Atrium and nearby rooms 8:00—8:45 After-dinner talk: Martin University Center (Fir Street) “Developing an undergraduate research program” Tom Price, The University of Akron 8:45 Business meeting -
Professor AO Kuku
CURRICULUM VITAE Professor A.O. Kuku I. Personal Details Date of Birth: March 20, 1941 Marital Status: Married with four children Nationality: Nigerian Sex: Male U.S.A. Permanent Resident (Green card) since March 2002 II CURRENT POSITION: Professor of Mathematics, Grambling State University, Grambling, LA, USA. Since August 2008 III. Position held in the last five years (a) Member, Institute for Advanced Study Princeton, NJ, USA. Sept. 2003-Aug. 2004 (b) Visiting Research Professor, MSRI Berkeley, CA, USA. Aug-Dec 2004 (c) Visiting Professor, OSU (Ohio State Univ.) Columbus, OH, USA 2005 (d) Distinguished Visiting Professor, Miami 2005 – 2006 University, Oxford, OH, USA (e) Visiting Professor, Universitat Bielefeld, Germany ,USA. 2006 (f) Visiting Professor, IHES, Paris, France 2006 (g) Visiting Professor, Max Planck Inst. Fur Mathematik, Bonn, Germany 2007 (h) Visiting Professor, National Mathema- tical Centre, Abuja, Nigeria. 2007 (i) Visiting professor, The University of Iowa, Iowa-City, USA 2007-2008 (j) Visiting Professor, National Mathema- Tical Centre, Abuja, Nigeria. 2008 IV. Educational Institutions Attended (University Education) 1.Makerere University College, Kampala, Uganda (then under special relationship with the University of London) 1962-1965 2.University of Ibadan, Nigeria 1966-1971 1 3Columbia University, New York City, USA (To write my Ph.D thesis) (Thesis written under Professor Hyman Bass) 1970-1971 V. Academic Qualification (with dates and granting bodies) 1.B. Sc (Special- Honours) Mathematics, University of London 1965 2.M. Sc. (Mathematics), University of Ibadan, Nigeria. 1968 3.Ph. D. (Mathematics), University of Ibadan, Nigeria 1971 (Thesis written under Professor Hyman Bass of Columbia Univerisity, New York). -
English 271.2: Literature for Young Children Fall 2013 Professor Jan Susina Class Meeting: Tuesday & Thursday 11:00-12:15 P.M
English 271.2: Literature for Young Children Fall 2013 Professor Jan Susina Class Meeting: Tuesday & Thursday 11:00-12:15 p.m. Class Room: Stevenson 347-B Office: Stevenson 402 Office Hours: Tuesday & Thursday 12:30-1:30 p.m. Office Phone: 438-3739 Email: [email protected] . Web site: http://ghostofthetalkingcricket.squarespace.com Tentative Syllabus: Aug. 20 Introduction and Overview to the Course Aug. 22 French Fairy Tales in M.C. Waldrep’s Favorite Fairy Tales: Perrault’s “Cinderella, or the Little Class Slipper,” “Little Red Riding-Hood,” “Toads and Diamonds,” “The Master Cat; or, Puss in Boots.” Madame De Villeneuve’s “Beauty and the Beast,” & Perrault’s “Sleeping Beauty in the Wood” (website) Aug. 27 German Folk Tales in M.C. Waldrep’s Favorite Fairy Tales: Grimm’s” Snowdrop [Snow White],” “Rapunzel,” “Rumplestiltkin,” “The Goose-Girl,” Grimm’s “Little Red-Cap” & “Hansel and Gretel” (website) Aug. 29 Hans Christian Andersen's Literary Fairy Tales in M.C. Waldrep’ Favorite Fairy Tales: “ How to Tell a True Princess (The Princess and the Pea),” “The Nightingale,” “The Ugly Ducking,” “The Story of the Emperor’s New Clothes,” & in Hans Christian Andersen’s The Little Mermaid and Other Fairy Tales “The Little Mermaid” “The Swineherd,” “The Steadfast Tin Soldier,” “The Little Match Girl” Deadline for Sign-up for Children’s Film for Film Paper Sept. 3 English Folk Tales in M.C, Waldrep’s Favorite Fairy Tales: “Jack and the Beanstalk,” “The Ratcatcher [Pied Piper of Hamelin],” & “Three Little Pigs” Sept. 5 American Fairy Tales: Walt Disney’s film adaptation of fairy tales: “Steamboat Willie” “The Three Little Pigs” “Snow White and the Seven “Dwarfs,” “Cinderella” & “The Little Mermaid” Sept. -
VITA Erica Flapan Department of Mathematics
VITA Erica Flapan Department of Mathematics (909) 621-8711 Pomona College 610 N. College Ave. Claremont, CA 91711, U.S.A. efl[email protected] http://pages.pomona.edu/ elf04747/ Education BA Hamilton College 1977 MA University of Wisconsin, Madison 1979 Ph.D University of Wisconsin, Madison 1983 Research Interests: 3-Manifolds, knot theory, topology of embedded graphs, applications of topology to chemistry and molecular biology Academic Positions 1983-1985, G.C. Evans Instructor, Rice University 1985-1986, Visiting Assistant Professor, University of California at Santa Barbara 1986-1990, Assistant Professor, Pomona College 1990-1998, Associate Professor, Pomona College 1998-present, Professor, Pomona College 2006-present, Lingurn H. Burkhead Professor, Pomona College Visiting Positions Fall 1987, Visiting Scholar, Universit´ede Paris-Sud, France Spring 1990, Visiting Scholar, Institute for Theoretical Dynamics, University of California at Davis Spring 1996, Research Associate, Institut Henri Poincar´e, France Fall 2000, Research Associate, Institut des Hautes Etudes´ Scientifiques, France Fall 2013, Long Term Visitor, Institute for Mathematics and its Applica- tions, University of Minnesota Spring 2015, Research Member in the Complementary Program, Mathemat- ical Sciences Research Institute National Awards and Honors 2011, Haimo Award for Distinguished College or University Teaching of Mathematics, Mathematical Association of America 2012, Inaugural Fellow of the American Mathematical Society 2015-2017, P´olya Lecturer of the Mathematical -
Program of the Sessions San Diego, California, January 9–12, 2013
Program of the Sessions San Diego, California, January 9–12, 2013 AMS Short Course on Random Matrices, Part Monday, January 7 I MAA Short Course on Conceptual Climate Models, Part I 9:00 AM –3:45PM Room 4, Upper Level, San Diego Convention Center 8:30 AM –5:30PM Room 5B, Upper Level, San Diego Convention Center Organizer: Van Vu,YaleUniversity Organizers: Esther Widiasih,University of Arizona 8:00AM Registration outside Room 5A, SDCC Mary Lou Zeeman,Bowdoin upper level. College 9:00AM Random Matrices: The Universality James Walsh, Oberlin (5) phenomenon for Wigner ensemble. College Preliminary report. 7:30AM Registration outside Room 5A, SDCC Terence Tao, University of California Los upper level. Angles 8:30AM Zero-dimensional energy balance models. 10:45AM Universality of random matrices and (1) Hans Kaper, Georgetown University (6) Dyson Brownian Motion. Preliminary 10:30AM Hands-on Session: Dynamics of energy report. (2) balance models, I. Laszlo Erdos, LMU, Munich Anna Barry*, Institute for Math and Its Applications, and Samantha 2:30PM Free probability and Random matrices. Oestreicher*, University of Minnesota (7) Preliminary report. Alice Guionnet, Massachusetts Institute 2:00PM One-dimensional energy balance models. of Technology (3) Hans Kaper, Georgetown University 4:00PM Hands-on Session: Dynamics of energy NSF-EHR Grant Proposal Writing Workshop (4) balance models, II. Anna Barry*, Institute for Math and Its Applications, and Samantha 3:00 PM –6:00PM Marina Ballroom Oestreicher*, University of Minnesota F, 3rd Floor, Marriott The time limit for each AMS contributed paper in the sessions meeting will be found in Volume 34, Issue 1 of Abstracts is ten minutes. -
Catalogo 2021 Orecchio Acerbo Editore
orecchio acerbo editore catalogo 2021 albi illustrati Noi umaNi uN lupo alla fiNEstra duE piccoli orsi NEW NEW NEW di Dieter Böge di Katerina Gorelik di Ylla illustrazioni Bernd Mölck-Tassel dai 3 anni in su | € 14.00 dai 3 anni in su | € 15.00 dai 5 anni in su | € 19.50 pp. 60 | cm. 23 x 28 pp. 40 | cm. 22 x 28 pp. 160 | cm. 17 x 21 ISBN 9788832070767 | Novembre 2021 ISBN 9788832070736 | Novembre 2021 ISBN 9788832070675 | Novembre 2021 ridErE E sorridErE Gli altri aNimali | GraNdi avvENturE GraNdi tEmi | raccoNtarE il prEsENtE Un quartiere che sembra molto tranquillo. Due piccoli orsi, fratello e sorella, si stanno Alcuni di noi possono fare cose incredibili, Abitato quasi solo da animali: c’è la signora affacciando per la prima volta dalla loro tana, parliamo oltre seimila lingue diverse e non Porcella, ottima cuoca, il dottor Topo, che spesso all’arrivo della primavera. La loro mamma sta per sempre ci capiamo, ma insieme possiamo riuscire visita a casa, il signor Pinguino, che sguazza nella andare in cerca di buon miele selvatico in imprese che nessun’altra creatura è in grado vasca e il signor Volpe che prepara la sua colazione e li ammonisce a non allontanarsi perché di affrontare. Possiamo essere crudeli o gentili, preferita. In quelle villette però ci abitano anche il mondo è ancora troppo grande per loro. Quelle curiosi o noiosi, felici o arrabbiati; c’è chi fa di un drago, una strega brava nel preparare pozioni raccomandazioni però vengono presto dimenticate tutto per trovare una casa o chi vive scoprendo e pure un lupo pieno di denti spesso passa di lì. -
Coefficients of the Solid Angle and Ehrhart Quasi-Polynomials
COEFFICIENTS OF THE SOLID ANGLE AND EHRHART QUASI-POLYNOMIALS FABR´ICIO CALUZA MACHADO AND SINAI ROBINS Abstract. Macdonald studied a discrete volume measure for a rational poly- tope P , called solid angle sum, that gives a natural discrete volume for P . We give a local formula for the codimension two quasi-coefficient of the solid angle sum of P . We also show how to recover the classical Ehrhart quasi-polynomial from the solid angle sum and in particular we find a similar local formula for the codimension one and codimension two quasi-coefficients. These local formulas are naturally valid for all positive real dilates of P . An interesting open question is to determine necessary and sufficient con- ditions on a polytope P for which the discrete volume of P given by the solid d angle sum equals its continuous volume: AP (t) = vol(P )t . We prove that d a sufficient condition is that P tiles R by translations, together with the Hyperoctahedral group. Contents 1. Introduction1 2. Main results4 3. Preliminaries9 4. Lattice sums 12 5. Proofs of Theorem 5.2 and Corollary 5.3 15 6. Obtaining the Ehrhart quasi-coefficients ed−1(t) and ed−2(t) 21 7. Two examples in three dimensions 26 8. Concrete polytopes and further remarks 31 References 34 Appendix A. Obtaining the solid angle quasi-coefficients from the Ehrhart quasi-coefficients 35 Appendix B. Comments about local formulas and SI-interpolators 38 1. Introduction d arXiv:1912.08017v2 [math.CO] 26 Jun 2020 Given a polytope P ⊆ R , the number of integer points within P can be regarded as a discrete analog of the volume of the body.