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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. -
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). -
Curriculum Vitae
CURRICULUM VITAE Professor Aderemi Oluyomi Kuku Ph.D, FAMS (USA), FTWAS, FAAS, FAS (Nig), FNMS, FMAN, FASI, OON, NNOM I. Personal Details Date of Birth: March 20, 1941 Marital Status: Married with four children Nationality: USA/Nigeria. Sex: Male II CONTACT ADDRESSES: Email [email protected] Website: www.aderemikuku.com MAILING ADDRESS: USA: 307 Penny Lane, Apt 5, Ruston, LA 71270, USA. NIGERIA(a) 2 Amure Street, Kongi-NewBodija, Ibadan, Oyo State, Nigeria. (b) Univerdityof Ibadan Post office Box 22574 Ibadan, Oyo State , Nigeria. PHONE NUMBERS: USA: +1-318-255-6433 Cell: +1-224-595-4854 NIGERIA: +234-70-56871969; +234-80-62329855 III. Positions held in the last 14 years (a) Member, Institute for Advanced Study Princeton, NJ, USA. Sept. 2003-Aug. 2004 (b) Visiting Research Professor, MSRI-- (Math. Sci. Research Inst) 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 2006 (f) Visiting Professor, IHES, Paris, France 2006 (g) Visiting Professor, Max Planck Inst. Fur Mathematik, Bonn, Germany 2007 1 (h) Distinguished Visiting Professor, National Mathematical Centre, Abuja, Nigeria. 2007 (i) Visiting Professor, The University of Iowa, Iowa-City, USA 2007-2008 (j) Professor of Mathematics, Grambling State University, Grambling, LA 71245, USA 2008-2009 (k) William W. S. Claytor Endowed Professor of Mathematics Grambling State University, Grambling, LA 71245, USA. 2009-2014 (l) Distinguished Visiting Professor, National Mathematical Centre, Abuja, Nigeria. Summer 2009, 2010,2011, 2012, 2013, 2014 (m) Distinguished Visiting Professor of Mathematics, IMSP—Institut demathematiques etde Sciences Physiques, Porto Novo, BeninRepublic,Nov/Dec,2015. -
Professor Peter Goldreich Member of the Board of Adjudicators Chairman of the Selection Committee for the Prize in Astronomy
The Shaw Prize The Shaw Prize is an international award to honour individuals who are currently active in their respective fields and who have recently achieved distinguished and significant advances, who have made outstanding contributions in academic and scientific research or applications, or who in other domains have achieved excellence. The award is dedicated to furthering societal progress, enhancing quality of life, and enriching humanity’s spiritual civilization. Preference is to be given to individuals whose significant work was recently achieved and who are currently active in their respective fields. Founder's Biographical Note The Shaw Prize was established under the auspices of Mr Run Run Shaw. Mr Shaw, born in China in 1907, was a native of Ningbo County, Zhejiang Province. He joined his brother’s film company in China in the 1920s. During the 1950s he founded the film company Shaw Brothers (HK) Limited in Hong Kong. He was one of the founding members of Television Broadcasts Limited launched in Hong Kong in 1967. Mr Shaw also founded two charities, The Shaw Foundation Hong Kong and The Sir Run Run Shaw Charitable Trust, both dedicated to the promotion of education, scientific and technological research, medical and welfare services, and culture and the arts. ~ 1 ~ Message from the Chief Executive I warmly congratulate the six Shaw Laureates of 2014. Established in 2002 under the auspices of Mr Run Run Shaw, the Shaw Prize is a highly prestigious recognition of the role that scientists play in shaping the development of a modern world. Since the first award in 2004, 54 leading international scientists have been honoured for their ground-breaking discoveries which have expanded the frontiers of human knowledge and made significant contributions to humankind. -
Algebraic Geometry of Topological Spaces I 3
ALGEBRAIC GEOMETRY OF TOPOLOGICAL SPACES I GUILLERMO CORTINAS˜ AND ANDREAS THOM Abstract. We use techniques from both real and complex algebraic geometry to study K- theoretic and related invariants of the algebra C(X) of continuous complex-valued functions on a compact Hausdorff topological space X. For example, we prove a parametrized version of a theorem of Joseph Gubeladze; we show that if M is a countable, abelian, cancella- tive, torsion-free, seminormal monoid, and X is contractible, then every finitely generated n projective module over C(X)[M] is free. The particular case M = N0 gives a parametrized version of the celebrated theorem proved independently by Daniel Quillen and Andrei Suslin that finitely generated projective modules over a polynomial ring over a field are free. The conjecture of Jonathan Rosenberg which predicts the homotopy invariance of the negative algebraic K-theory of C(X) follows from the particular case M = Zn. We also give alge- braic conditions for a functor from commutative algebras to abelian groups to be homotopy invariant on C∗-algebras, and for a homology theory of commutative algebras to vanish on C∗-algebras. These criteria have numerous applications. For example, the vanishing cri- terion applied to nil-K-theory implies that commutative C∗-algebras are K-regular. As another application, we show that the familiar formulas of Hochschild-Kostant-Rosenberg and Loday-Quillen for the algebraic Hochschild and cyclic homology of the coordinate ring of a smooth algebraic variety remain valid for the algebraic Hochschild and cyclic homology of C(X). Applications to the conjectures of Be˘ılinson-Soul´eand Farrell-Jones are also given. -
Lecture Notes in Mathematics
Lecture Notes in Mathematics Edited by A. Dold and 13. Eckmann 551 Algebraic K-Theory Proceedings of the Conference Held at Northwestern University Evanston, January 12-16, 1976 Edited by Michael R. Stein Springer-Verlag Berlin. Heidelberg- New York 19 ? 6 Editor Michael R. Stein Department of Mathematics Northwestern University Evanston, I1. 60201/USA Library of Congress Cataloging in Publication Data Main entry under title: Algebraic K-theory. (Lecture notes in mathematics ; 551) Bibliography: p. Includes index. i. K-theory--Congresses. 2 ~ Homology theory-- Congresses. 3. Rings (Algebra)--Congresses. I. Stein, M~chael R., 1943- II. Series: Lecture notes in mathematics (Berlin) ; 551. QAB,I,q8 no. 551 [QA61~.33] 510'.8s [514'.23] 76-~9894 ISBN AMS Subject Classifications (1970): 13D15, 14C99,14 F15,16A54,18 F25, 18H10, 20C10, 20G05, 20G35, 55 El0, 57A70 ISBN 3-540-07996-3 Springer-Verlag Berlin 9Heidelberg 9New York ISBN 0-38?-0?996-3 Springer-Verlag New York 9Heidelberg 9Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, re- printing, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under w 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. 9 by Springer-Verlag Berlin 9Heidelberg 1976 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. Introduction A conference on algebraic K-theory, jointly supported by the National Science Foundation and Northwestern University, was held at Northwestern University January 12-16, 1976. -
Order-Of-Magnitude Physics: Understanding the World with Dimensional Analysis, Educated Guesswork, and White Lies Peter Goldreic
Order-of-Magnitude Physics: Understanding the World with Dimensional Analysis, Educated Guesswork, and White Lies Peter Goldreich, California Institute of Technology Sanjoy Mahajan, University of Cambridge Sterl Phinney, California Institute of Technology Draft of 1 August 1999 c 1999 Send comments to [email protected] ii Contents 1 Wetting Your Feet 1 1.1 Warmup problems 1 1.2 Scaling analyses 13 1.3 What you have learned 21 2 Dimensional Analysis 23 2.1 Newton’s law 23 2.2 Pendula 27 2.3 Drag in fluids 31 2.4 What you have learned 41 3 Materials I 43 3.1 Sizes 43 3.2 Energies 51 3.3 Elastic properties 53 3.4 Application to white dwarfs 58 3.5 What you have learned 62 4 Materials II 63 4.1 Thermal expansion 63 4.2 Phase changes 65 4.3 Specific heat 73 4.4 Thermal diffusivity of liquids and solids 77 4.5 Diffusivity and viscosity of gases 79 4.6 Thermal conductivity 80 4.7 What you have learned 83 5 Waves 85 5.1 Dispersion relations 85 5.2 Deep water 88 5.3 Shallow water 106 5.4 Combining deep- and shallow-water gravity waves 108 5.5 Combining deep- and shallow-water ripples 108 5.6 Combining all the analyses 109 5.7 What we did 109 Bibliography 110 1 1 Wetting Your Feet Most technical education emphasizes exact answers. If you are a physicist, you solve for the energy levels of the hydrogen atom to six decimal places. If you are a chemist, you measure reaction rates and concentrations to two or three decimal places. -
Arxiv:1111.3682V1 [Astro-Ph.EP] 15 Nov 2011 Ant Planets, As Well As Their Dynamical Architecture (I.E
Draft version November 17, 2011 Preprint typeset using LATEX style emulateapj v. 11/10/09 INSTABILITY-DRIVEN DYNAMICAL EVOLUTION MODEL OF A PRIMORDIALLY 5 PLANET OUTER SOLAR SYSTEM Konstantin Batygin1, Michael E. Brown1 & Hayden Betts2 1Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125 and 2Polytechnic School, Pasadena, CA 91106 Draft version November 17, 2011 ABSTRACT Over the last decade, evidence has mounted that the solar system's observed state can be favorably reproduced in the context of an instability-driven dynamical evolution model, such as the \Nice" model. To date, all successful realizations of instability models have concentrated on evolving the four giant planets onto their current orbits from a more compact configuration. Simultaneously, the possibility of forming and ejecting additional planets has been discussed, but never successfully implemented. Here we show that a large array of 5-planet (2 gas giants + 3 ice giants) multi-resonant initial states can lead to an adequate formation of the outer solar system, featuring an ejection of an ice giant during a phase of instability. Particularly, our simulations demonstrate that the eigenmodes which characterize the outer solar system's secular dynamics can be closely matched with a 5-planet model. Furthermore, provided that the ejection timescale of the extra planet is short, orbital excitation of a primordial cold classical Kuiper belt can also be avoided in this scenario. Thus the solar system is one of many possible outcomes of dynamical relaxation and can originate from a wide variety of initial states. This deems the construction of a unique model of solar system's early dynamical evolution impossible. -
Quillen's Work in Algebraic K-Theory
J. K-Theory 11 (2013), 527–547 ©2013 ISOPP doi:10.1017/is012011011jkt203 Quillen’s work in algebraic K-theory by DANIEL R. GRAYSON Abstract We survey the genesis and development of higher algebraic K-theory by Daniel Quillen. Key Words: higher algebraic K-theory, Quillen. Mathematics Subject Classification 2010: 19D99. Introduction This paper1 is dedicated to the memory of Daniel Quillen. In it, we examine his brilliant discovery of higher algebraic K-theory, including its roots in and genesis from topological K-theory and ideas connected with the proof of the Adams conjecture, and his development of the field into a complete theory in just a few short years. We provide a few references to further developments, including motivic cohomology. Quillen’s main work on algebraic K-theory appears in the following papers: [65, 59, 62, 60, 61, 63, 55, 57, 64]. There are also the papers [34, 36], which are presentations of Quillen’s results based on hand-written notes of his and on communications with him, with perhaps one simplification and several inaccuracies added by the author. Further details of the plus-construction, presented briefly in [57], appear in [7, pp. 84–88] and in [77]. Quillen’s work on Adams operations in higher algebraic K-theory is exposed by Hiller in [45, sections 1-5]. Useful surveys of K-theory and related topics include [81, 46, 38, 39, 67] and any chapter in Handbook of K-theory [27]. I thank Dale Husemoller, Friedhelm Waldhausen, Chuck Weibel, and Lars Hesselholt for useful background information and advice. 1. -
References Is Provisional, and Will Grow (Or Shrink) As the Course Progresses
Note: This list of references is provisional, and will grow (or shrink) as the course progresses. It will never be comprehensive. See also the references (and the book) in the online version of Weibel's K- Book [40] at http://www.math.rutgers.edu/ weibel/Kbook.html. References [1] Armand Borel and Jean-Pierre Serre. Le th´eor`emede Riemann-Roch. Bull. Soc. Math. France, 86:97{136, 1958. [2] A. K. Bousfield. The localization of spaces with respect to homology. Topology, 14:133{150, 1975. [3] A. K. Bousfield and E. M. Friedlander. Homotopy theory of Γ-spaces, spectra, and bisimplicial sets. In Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), II, volume 658 of Lecture Notes in Math., pages 80{130. Springer, Berlin, 1978. [4] Kenneth S. Brown and Stephen M. Gersten. Algebraic K-theory as gen- eralized sheaf cohomology. In Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), pages 266{ 292. Lecture Notes in Math., Vol. 341. Springer, Berlin, 1973. [5] William Dwyer, Eric Friedlander, Victor Snaith, and Robert Thoma- son. Algebraic K-theory eventually surjects onto topological K-theory. Invent. Math., 66(3):481{491, 1982. [6] Eric M. Friedlander and Daniel R. Grayson, editors. Handbook of K- theory. Vol. 1, 2. Springer-Verlag, Berlin, 2005. [7] Ofer Gabber. K-theory of Henselian local rings and Henselian pairs. In Algebraic K-theory, commutative algebra, and algebraic geometry (Santa Margherita Ligure, 1989), volume 126 of Contemp. Math., pages 59{70. Amer. Math. Soc., Providence, RI, 1992. [8] Henri Gillet and Daniel R. -
Prize Is Awarded Every Three Years at the Joint Mathematics Meetings
AMERICAN MATHEMATICAL SOCIETY LEVI L. CONANT PRIZE This prize was established in 2000 in honor of Levi L. Conant to recognize the best expository paper published in either the Notices of the AMS or the Bulletin of the AMS in the preceding fi ve years. Levi L. Conant (1857–1916) was a math- ematician who taught at Dakota School of Mines for three years and at Worcester Polytechnic Institute for twenty-fi ve years. His will included a bequest to the AMS effective upon his wife’s death, which occurred sixty years after his own demise. Citation Persi Diaconis The Levi L. Conant Prize for 2012 is awarded to Persi Diaconis for his article, “The Markov chain Monte Carlo revolution” (Bulletin Amer. Math. Soc. 46 (2009), no. 2, 179–205). This wonderful article is a lively and engaging overview of modern methods in probability and statistics, and their applications. It opens with a fascinating real- life example: a prison psychologist turns up at Stanford University with encoded messages written by prisoners, and Marc Coram uses the Metropolis algorithm to decrypt them. From there, the article gets even more compelling! After a highly accessible description of Markov chains from fi rst principles, Diaconis colorfully illustrates many of the applications and venues of these ideas. Along the way, he points to some very interesting mathematics and some fascinating open questions, especially about the running time in concrete situ- ations of the Metropolis algorithm, which is a specifi c Monte Carlo method for constructing Markov chains. The article also highlights the use of spectral methods to deduce estimates for the length of the chain needed to achieve mixing. -
A Journal of the K-Theory Foundation(Ktheoryfoundation.Org)
ANNALSOF K-THEORY Paul Balmer Spencer Bloch no. 1 vol. 1 2016 Alain Connes Guillermo Cortiñas Eric Friedlander Max Karoubi Gennadi Kasparov Alexander Merkurjev Amnon Neeman Jonathan Rosenberg Marco Schlichting Andrei Suslin Vladimir Voevodsky Charles Weibel Guoliang Yu msp A JOURNAL OF THE K-THEORY FOUNDATION ANNALS OF K-THEORY msp.org/akt EDITORIAL BOARD Paul Balmer University of California, Los Angeles, USA [email protected] Spencer Bloch University of Chicago, USA [email protected] Alain Connes Collège de France; Institut des Hautes Études Scientifiques; Ohio State University [email protected] Guillermo Cortiñas Universidad de Buenos Aires and CONICET, Argentina [email protected] Eric Friedlander University of Southern California, USA [email protected] Max Karoubi Institut de Mathématiques de Jussieu – Paris Rive Gauche, France [email protected] Gennadi Kasparov Vanderbilt University, USA [email protected] Alexander Merkurjev University of California, Los Angeles, USA [email protected] Amnon Neeman amnon.Australian National University [email protected] Jonathan Rosenberg (Managing Editor) University of Maryland, USA [email protected] Marco Schlichting University of Warwick, UK [email protected] Andrei Suslin Northwestern University, USA [email protected] Vladimir Voevodsky Institute for Advanced Studies, USA [email protected] Charles Weibel (Managing Editor) Rutgers University, USA [email protected] Guoliang Yu Texas A&M University, USA [email protected] PRODUCTION Silvio Levy (Scientific Editor) [email protected] Annals of K-Theory is a journal of the K-Theory Foundation(ktheoryfoundation.org). The K-Theory Foundation acknowledges the precious support of Foundation Compositio Mathematica, whose help has been instrumental in the launch of the Annals of K-Theory.