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2006 Annual Report
Contents Clay Mathematics Institute 2006 James A. Carlson Letter from the President 2 Recognizing Achievement Fields Medal Winner Terence Tao 3 Persi Diaconis Mathematics & Magic Tricks 4 Annual Meeting Clay Lectures at Cambridge University 6 Researchers, Workshops & Conferences Summary of 2006 Research Activities 8 Profile Interview with Research Fellow Ben Green 10 Davar Khoshnevisan Normal Numbers are Normal 15 Feature Article CMI—Göttingen Library Project: 16 Eugene Chislenko The Felix Klein Protocols Digitized The Klein Protokolle 18 Summer School Arithmetic Geometry at the Mathematisches Institut, Göttingen, Germany 22 Program Overview The Ross Program at Ohio State University 24 PROMYS at Boston University Institute News Awards & Honors 26 Deadlines Nominations, Proposals and Applications 32 Publications Selected Articles by Research Fellows 33 Books & Videos Activities 2007 Institute Calendar 36 2006 Another major change this year concerns the editorial board for the Clay Mathematics Institute Monograph Series, published jointly with the American Mathematical Society. Simon Donaldson and Andrew Wiles will serve as editors-in-chief, while I will serve as managing editor. Associate editors are Brian Conrad, Ingrid Daubechies, Charles Fefferman, János Kollár, Andrei Okounkov, David Morrison, Cliff Taubes, Peter Ozsváth, and Karen Smith. The Monograph Series publishes Letter from the president selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. The next volume in the series will be Ricci Flow and the Poincaré Conjecture, by John Morgan and Gang Tian. Their book will appear in the summer of 2007. In related publishing news, the Institute has had the complete record of the Göttingen seminars of Felix Klein, 1872–1912, digitized and made available on James Carlson. -
UNESCO Kalinga Prize Winner – 1992 Dr. Jorge Flores Valdes
Glossary on Kalinga Prize Laureates UNESCO Kalinga Prize Winner – 1992 Dr. Jorge Flores Valdes Great Science Popularizer of Mexico [ Born: February 1st , 1941 ……….. ] The Physics is wonderful and if at this point of my life they returned to ask to me, like when it was in sixth degree of Primary, what I want to be, it would say that Physical” …Jorge Flores Valdes 1 Glossary on Kalinga Prize Laureates 2 Glossary on Kalinga Prize Laureates BIOGRAPHICAL DATA DR. JORGE FLORES June, 2007 Jorge Flores was born in Mexico City, Mexico, on used the mathematical techniques they had February 1st, 1941. He obtained a bachelor’s degree developed to analyze quantum systems to formulate in 1962 and a Ph. D. degree in Physics in 1965, a model for the seismic response of sedimentary both degrees from the Universidad Nacional basins. The paper was published in 1987 in the Autónoma de México, UNAM (National University prestigious journal Nature; the front page of the of Mexico). From 1965 to 1967 he was a corresponding issue was dedicated to this article. postdoctoral fellow at Princeton University; in 1969 Dr. Flores went on publishing on seismology, using he worked at the International Centre for Theoretical his model, which up to the present seems to be the Physics in Trieste and in 1970 he was visiting only plausible explanation of this disastrous effect. professor at the Université de Paris (Orsay). In the year 2000 he established a laboratory to study He published his first paper in the journal Nuclear the vibration of elastic systems. Together with a Physics A in 1963. -
Deloitte Legal Experience the Future of Law, Today
Deloitte Legal Experience the future of law, today Latin America 2021 Deloitte Legal—Experience the future of law, today | Latin America 2021 Deloitte Legal—Experience the future of law, today | Latin America 2021 About Deloitte Legal 04 Deloitte Legal global coverage 06 Pioneering and pragmatic solutions 08 Argentina 11 Brazil 12 Chile 13 Colombia 14 Costa Rica 15 Dominican Republic 16 Ecuador 17 El Salvador 18 Guatemala 19 Honduras 20 Mexico 21 Nicaragua 22 Paraguay 23 Peru 24 Uruguay 25 Venezuela 26 Deloitte Legal services 28 02 03 Deloitte Legal—Experience the future of law, today | Latin America 2021 Deloitte Legal—Experience the future of law, today | Latin America 2021 Experience the future of law, today Deloitte Legal What we deliver More than operating in over For family-owned small and medium-sized companies, listed stock corporations, or international groups of companies, Deloitte Legal helps our clients face the challenges of an ever-changing regulatory and 2,500 80 economic environment. legal professionals countries Perspective that is global, yet grounded Deloitte Legal works with clients globally to help them resolve their present challenges and plan for the future. Our industry knowledge, global footprint, and multidisciplinary service model result in a strategic perspective that enables and empowers our clients to meet their local responsibilities and collaborating seamlessly thrive in the global marketplace. across borders and with other Deloitte business lines Cross-border coordination and a single point of contact It can be enormously challenging to manage numerous legal services providers around the world and issues can slip through the cracks. As one of the global leaders in legal services, Deloitte Legal works with you to As part of the global Deloitte professional services network, Deloitte Legal collaborates with colleagues in an array of understand your needs and your vision, and to coordinate delivery around the globally integrated services to deliver multinational legal solutions that are: world to help you achieve your business goals. -
The Physical Basis of the Direction of Time (The Frontiers Collection), 5Th
the frontiers collection the frontiers collection Series Editors: A.C. Elitzur M.P. Silverman J. Tuszynski R. Vaas H.D. Zeh The books in this collection are devoted to challenging and open problems at the forefront of modern science, including related philosophical debates. In contrast to typical research monographs, however, they strive to present their topics in a manner accessible also to scientifically literate non-specialists wishing to gain insight into the deeper implications and fascinating questions involved. Taken as a whole, the series reflects the need for a fundamental and interdisciplinary approach to modern science. Furthermore, it is intended to encourage active scientists in all areas to ponder over important and perhaps controversial issues beyond their own speciality. Extending from quantum physics and relativity to entropy, consciousness and complex systems – the Frontiers Collection will inspire readers to push back the frontiers of their own knowledge. InformationandItsRoleinNature The Thermodynamic By J. G. Roederer Machinery of Life By M. Kurzynski Relativity and the Nature of Spacetime By V. Petkov The Emerging Physics of Consciousness Quo Vadis Quantum Mechanics? Edited by J. A. Tuszynski Edited by A. C. Elitzur, S. Dolev, N. Kolenda Weak Links Life – As a Matter of Fat Stabilizers of Complex Systems The Emerging Science of Lipidomics from Proteins to Social Networks By O. G. Mouritsen By P. Csermely Quantum–Classical Analogies Mind, Matter and the Implicate Order By D. Dragoman and M. Dragoman By P.T.I. Pylkkänen Knowledge and the World Quantum Mechanics at the Crossroads Challenges Beyond the Science Wars New Perspectives from History, Edited by M. -
Two Arrows of Time in Nonlocal Particle Dynamics
Two Arrows of Time in Nonlocal Particle Dynamics Roderich Tumulka∗ July 21, 2007 Abstract Considering what the world would be like if backwards causation were possible is usually mind-bending. Here I discuss something that is easier to study: a toy model that incorporates a very restricted sort of backwards causation. It defines particle world lines by means of a kind of differential delay equation with negative delay. The model pre- sumably prohibits signalling to the past and superluminal signalling, but allows nonlocality while being fully covariant. And that is what constitutes the model’s value: it is an explicit example of the possi- bility of Lorentz invariant nonlocality. That is surprising in so far as many authors thought that nonlocality, in particular nonlocal laws for particle world lines, must conflict with relativity. The development of this model was inspired by the search for a fully covariant version of Bohmian mechanics. arXiv:quant-ph/0210207v2 18 Sep 2008 In this paper I will introduce to you a dynamical system—a law of mo- tion for point particles—that has been invented [5] as a toy model based on Bohmian mechanics. Bohmian mechanics is a version of quantum mechanics with particle trajectories; see [4] for an introduction and overview. What makes this toy model remarkable is that it has two arrows of time, and that precisely its having two arrows of time is what allows it to perform what it was designed for: to have effects travel faster than light from their causes (in short, nonlocality) without breaking Lorentz invariance. Why should anyone ∗Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA. -
Finslerian Geometries Fundamental Theories of Physics
Finslerian Geometries Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE, University of Denver, U.S.A. Editorial Advisory Board: LAWRENCE P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, u.K. CLIVE KILMISTER, University of London, U.K. PEKKA J. LAHTI, University of Turku, Finland GUNTER LUDWIG, Philipps-Universitiit, Marburg, Germany NATHAN ROSEN, Israel Institute of Technology, Israel ASHER PERES, Israel Institute of Technology, Israel EDUARD PRUGOVECKI, University of Toronto, Canada MENDEL SACHS, State University of New York at Buffalo, U.S.A. ABDUS SALAM, International Centre for Theoretical Physics, Trieste, Italy HANS-JURGEN TREDER, Zentralinstitut fur Astrophysik der Akademie der Wissenschaften, Germany Volume 109 Finslerian Geometries A Meeting of Minds edited by P.L. Antonell i DeJXlrlmem of Mathematical Sciences, University ofAlberta, EdmonlOn. Alberta, Canada SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A C .I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-94-010-5838-4 ISBN 978-94-011-4235-9 (eBook) DOI 10.1007/978-94-011-4235-9 Printed an arid1ree paper AH Rights Reserved © 2000 Springer Science+Business Media Dordrecht Originally published by K!uwer Academic Publishers in 2000 Soticovcr repri Il! of the hardcover l s( cd ition in 20()(} No part of the material protected by this copyright natice may be reproduced Of utilized in any farm Of by any means, electronic or mechanical, induding pholocopying, recording or by any informat ion slorage and relrieval system, withoUI wrinen permissian from the copyright owner. -
Defining Physics at Imaginary Time: Reflection Positivity for Certain
Defining physics at imaginary time: reflection positivity for certain Riemannian manifolds A thesis presented by Christian Coolidge Anderson [email protected] (978) 204-7656 to the Department of Mathematics in partial fulfillment of the requirements for an honors degree. Advised by Professor Arthur Jaffe. Harvard University Cambridge, Massachusetts March 2013 Contents 1 Introduction 1 2 Axiomatic quantum field theory 2 3 Definition of reflection positivity 4 4 Reflection positivity on a Riemannian manifold M 7 4.1 Function space E over M ..................... 7 4.2 Reflection on M .......................... 10 4.3 Reflection positive inner product on E+ ⊂ E . 11 5 The Osterwalder-Schrader construction 12 5.1 Quantization of operators . 13 5.2 Examples of quantizable operators . 14 5.3 Quantization domains . 16 5.4 The Hamiltonian . 17 6 Reflection positivity on the level of group representations 17 6.1 Weakened quantization condition . 18 6.2 Symmetric local semigroups . 19 6.3 A unitary representation for Glor . 20 7 Construction of reflection positive measures 22 7.1 Nuclear spaces . 23 7.2 Construction of nuclear space over M . 24 7.3 Gaussian measures . 27 7.4 Construction of Gaussian measure . 28 7.5 OS axioms for the Gaussian measure . 30 8 Reflection positivity for the Laplacian covariance 31 9 Reflection positivity for the Dirac covariance 34 9.1 Introduction to the Dirac operator . 35 9.2 Proof of reflection positivity . 38 10 Conclusion 40 11 Appendix A: Cited theorems 40 12 Acknowledgments 41 1 Introduction Two concepts dominate contemporary physics: relativity and quantum me- chanics. They unite to describe the physics of interacting particles, which live in relativistic spacetime while exhibiting quantum behavior. -
A Scale-Covariant Quantum Space-Time
A scale-covariant quantum space-time Claudio Perini∗ Institute for Gravitation and the Cosmos, Physics Department, Penn State, University Park, PA 16802-6300, USA Gabriele Nunzio Tornetta† School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, G12 8QW, Scotland A noncommutative space-time admitting dilation symmetry was briefly mentioned in the seminal work [1] of Doplicher, Fredenhagen and Roberts. In this paper we explicitly construct the model in details and carry out an in-depth analysis. The C∗-algebra that describes this quantum space-time is determined, and it is shown that it admits an action by - automorphisms of the dilation group, along with the expected Poincar´ecovariance. In order∗ to study the main physical properties of this scale-covariant model, a free scalar neutral field is introduced as a investigation tool. Our key results are then the loss of locality and the irreducibility, or triviality, of special field algebras associated with regions of the ordinary Minkowski space-time. It turns out, in the conclusions, that this analysis allows also to argue on viable ways of constructing a full conformally covariant model for quantum space-time. I. INTRODUCTION In this paper we study a non-commutative space-time of DFR-type, that can be obtained as the limiting scale-free case of the original DFR model [1]. The main mathematical interest to study this model is that it is Poincar´e and dilation covariant, thus it possesses almost all the symmetries given by the conformal group. The issue of implementing the remaining symmetry, which is the relativistic ray inversion, is discussed in the concluding section. -
Mathematisches Forschungsinstitut Oberwolfach Reflection Positivity
Mathematisches Forschungsinstitut Oberwolfach Report No. 55/2017 DOI: 10.4171/OWR/2017/55 Reflection Positivity Organised by Arthur Jaffe, Harvard Karl-Hermann Neeb, Erlangen Gestur Olafsson, Baton Rouge Benjamin Schlein, Z¨urich 26 November – 2 December 2017 Abstract. The main theme of the workshop was reflection positivity and its occurences in various areas of mathematics and physics, such as Representa- tion Theory, Quantum Field Theory, Noncommutative Geometry, Dynamical Systems, Analysis and Statistical Mechanics. Accordingly, the program was intrinsically interdisciplinary and included talks covering different aspects of reflection positivity. Mathematics Subject Classification (2010): 17B10, 22E65, 22E70, 81T08. Introduction by the Organisers The workshop on Reflection Positivity was organized by Arthur Jaffe (Cambridge, MA), Karl-Hermann Neeb (Erlangen), Gestur Olafsson´ (Baton Rouge) and Ben- jamin Schlein (Z¨urich) during the week November 27 to December 1, 2017. The meeting was attended by 53 participants from all over the world. It was organized around 24 lectures each of 50 minutes duration representing major recent advances or introducing to a specific aspect or application of reflection positivity. The meeting was exciting and highly successful. The quality of the lectures was outstanding. The exceptional atmosphere of the Oberwolfach Institute provided the optimal environment for bringing people from different areas together and to create an atmosphere of scientific interaction and cross-fertilization. In particular, people from different subcommunities exchanged ideas and this lead to new col- laborations that will probably stimulate progress in unexpected directions. 3264 Oberwolfach Report 55/2017 Reflection positivity (RP) emerged in the early 1970s in the work of Osterwalder and Schrader as one of their axioms for constructive quantum field theory ensuring the equivalence of their euclidean setup with Wightman fields. -
Partial Differential Equations
CALENDAR OF AMS MEETINGS THIS CALENDAR lists all meetings which have been approved by the Council pnor to the date this issue of the Nouces was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcement and the list of organizers of special sessions. MEETING ABSTRACT NUMBER DATE PLACE DEADLINE ISSUE 778 June 20-21, 1980 Ellensburg, Washington APRIL 21 June 1980 779 August 18-22, 1980 Ann Arbor, Michigan JUNE 3 August 1980 (84th Summer Meeting) October 17-18, 1980 Storrs, Connecticut October 31-November 1, 1980 Kenosha, Wisconsin January 7-11, 1981 San Francisco, California (87th Annual Meeting) January 13-17, 1982 Cincinnati, Ohio (88th Annual Meeting) Notices DEADLINES ISSUE NEWS ADVERTISING June 1980 April 18 April 29 August 1980 June 3 June 18 Deadlines for announcements intended for the Special Meetings section are the same as for News. -
6. L CPT Reversal
6. CPT reversal l Précis. On the representation view, there may be weak and strong arrows of time. A weak arrow exists. A strong arrow might too, but not in current physics due to CPT symmetry. There are many ways to reverse time besides the time reversal operator T. Writing P for spatial reflection or ‘parity’, and C for matter-antimatter exchange or ‘charge conjugation’, we find that PT, CT, and CPT are all time reversing transformations, when they exist. More generally, for any non-time-reversing (unitary) transformation U, we find that UT is time reversing. Are any of these transformations relevant for the arrow of time? Feynman (1949) captured many of our imaginations with the proposal that to understand the direction of time, we must actually consider the exchange of matter and antimatter as well.1 Writing about it years later, he said: “A backwards-moving electron when viewed with time moving forwards appears the same as an ordinary electron, except it’s attracted to normal electrons — we say it has positive charge. For this reason it’s called a ‘positron’. The positron is a sister to the electron, and it is an example of an ‘anti-particle’. This phenomenon is quite general. Every particle in Nature has an amplitude to move backwards in time, and therefore has an anti-particle.”(Feynman 1985, p.98) Philosophers Arntzenius and Greaves (2009, p.584) have defended Feynman’s proposal, 1In his Nobel prize speech, Feynman (1972, pg.163) attributes this idea to Wheeler in the development of their absorber theory (Wheeler and Feynman 1945). -
Dark Matter and Weak Signals of Quantum Spacetime
PHYSICAL REVIEW D 95, 065009 (2017) Dark matter and weak signals of quantum spacetime † ‡ Sergio Doplicher,1,* Klaus Fredenhagen,2, Gerardo Morsella,3, and Nicola Pinamonti4,§ 1Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy 2II Institut für Theoretische Physik, Universität Hamburg, D-22761 Hamburg, Germany 3Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133 Roma, Italy 4Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, I-16146 Genova, Italy, and INFN Sezione di Genova, Genova, Italy (Received 29 December 2016; published 13 March 2017) In physically motivated models of quantum spacetime, a Uð1Þ gauge theory turns into a Uð∞Þ gauge theory; hence, free classical electrodynamics is no longer free and neutral fields may have electromagnetic interactions. We discuss the last point for scalar fields, as a way to possibly describe dark matter; we have in mind the gravitational collapse of binary systems or future applications to self-gravitating Bose-Einstein condensates as possible sources of evidence of quantum gravitational phenomena. The effects considered so far, however, seem too faint to be detectable at present. DOI: 10.1103/PhysRevD.95.065009 I. INTRODUCTION but their superpositions would, in general, not be—they would lose energy in favor of mysterious massive modes One of the main difficulties of present-day physics is the (see also [6]). lack of observation of quantum aspects of gravity. Quantum A naive computation showed, by that mechanism, that a gravity has to be searched without a guide from nature; the monochromatic wave train passing through a partially observed universe must be explained as carrying traces of reflecting mirror should lose, in favor of those ghost quantum gravitational phenomena in the only “laboratory” modes, a fraction of its energy—a very small fraction, suitable to those effects, i.e., the universe itself a few unfortunately, of the order of one part in 10−130 [5].