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String Theory. Volume 1, Introduction to the Bosonic String
This page intentionally left blank String Theory, An Introduction to the Bosonic String The two volumes that comprise String Theory provide an up-to-date, comprehensive, and pedagogic introduction to string theory. Volume I, An Introduction to the Bosonic String, provides a thorough introduction to the bosonic string, based on the Polyakov path integral and conformal field theory. The first four chapters introduce the central ideas of string theory, the tools of conformal field theory and of the Polyakov path integral, and the covariant quantization of the string. The next three chapters treat string interactions: the general formalism, and detailed treatments of the tree-level and one loop amplitudes. Chapter eight covers toroidal compactification and many important aspects of string physics, such as T-duality and D-branes. Chapter nine treats higher-order amplitudes, including an analysis of the finiteness and unitarity, and various nonperturbative ideas. An appendix giving a short course on path integral methods is also included. Volume II, Superstring Theory and Beyond, begins with an introduction to supersym- metric string theories and goes on to a broad presentation of the important advances of recent years. The first three chapters introduce the type I, type II, and heterotic superstring theories and their interactions. The next two chapters present important recent discoveries about strongly coupled strings, beginning with a detailed treatment of D-branes and their dynamics, and covering string duality, M-theory, and black hole entropy. A following chapter collects many classic results in conformal field theory. The final four chapters are concerned with four-dimensional string theories, and have two goals: to show how some of the simplest string models connect with previous ideas for unifying the Standard Model; and to collect many important and beautiful general results on world-sheet and spacetime symmetries. -
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. -
Stephen Hawking: 'There Are No Black Holes' Notion of an 'Event Horizon', from Which Nothing Can Escape, Is Incompatible with Quantum Theory, Physicist Claims
NATURE | NEWS Stephen Hawking: 'There are no black holes' Notion of an 'event horizon', from which nothing can escape, is incompatible with quantum theory, physicist claims. Zeeya Merali 24 January 2014 Artist's impression VICTOR HABBICK VISIONS/SPL/Getty The defining characteristic of a black hole may have to give, if the two pillars of modern physics — general relativity and quantum theory — are both correct. Most physicists foolhardy enough to write a paper claiming that “there are no black holes” — at least not in the sense we usually imagine — would probably be dismissed as cranks. But when the call to redefine these cosmic crunchers comes from Stephen Hawking, it’s worth taking notice. In a paper posted online, the physicist, based at the University of Cambridge, UK, and one of the creators of modern black-hole theory, does away with the notion of an event horizon, the invisible boundary thought to shroud every black hole, beyond which nothing, not even light, can escape. In its stead, Hawking’s radical proposal is a much more benign “apparent horizon”, “There is no escape from which only temporarily holds matter and energy prisoner before eventually a black hole in classical releasing them, albeit in a more garbled form. theory, but quantum theory enables energy “There is no escape from a black hole in classical theory,” Hawking told Nature. Peter van den Berg/Photoshot and information to Quantum theory, however, “enables energy and information to escape from a escape.” black hole”. A full explanation of the process, the physicist admits, would require a theory that successfully merges gravity with the other fundamental forces of nature. -
Anomalies, Dualities, and Topology of D = 6 N = 1 Superstring Vacua
RU-96-16 NSF-ITP-96-21 CALT-68-2057 IASSNS-HEP-96/53 hep-th/9605184 Anomalies, Dualities, and Topology of D =6 N =1 Superstring Vacua Micha Berkooz,1 Robert G. Leigh,1 Joseph Polchinski,2 John H. Schwarz,3 Nathan Seiberg,1 and Edward Witten4 1Department of Physics, Rutgers University, Piscataway, NJ 08855-0849 2Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030 3California Institute of Technology, Pasadena, CA 91125 4Institute for Advanced Study, Princeton, NJ 08540 Abstract We consider various aspects of compactifications of the Type I/heterotic Spin(32)/Z2 theory on K3. One family of such compactifications in- cludes the standard embedding of the spin connection in the gauge group, and is on the same moduli space as the compactification of arXiv:hep-th/9605184v1 25 May 1996 the heterotic E8 × E8 theory on K3 with instanton numbers (8,16). Another class, which includes an orbifold of the Type I theory re- cently constructed by Gimon and Polchinski and whose field theory limit involves some topological novelties, is on the moduli space of the heterotic E8 × E8 theory on K3 with instanton numbers (12,12). These connections between Spin(32)/Z2 and E8 × E8 models can be demonstrated by T duality, and permit a better understanding of non- perturbative gauge fields in the (12,12) model. In the transformation between Spin(32)/Z2 and E8 × E8 models, the strong/weak coupling duality of the (12,12) E8 × E8 model is mapped to T duality in the Type I theory. The gauge and gravitational anomalies in the Type I theory are canceled by an extension of the Green-Schwarz mechanism. -
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). -
Eternal Inflation and Its Implications
IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL J. Phys. A: Math. Theor. 40 (2007) 6811–6826 doi:10.1088/1751-8113/40/25/S25 Eternal inflation and its implications Alan H Guth Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA E-mail: [email protected] Received 8 February 2006 Published 6 June 2007 Online at stacks.iop.org/JPhysA/40/6811 Abstract Isummarizetheargumentsthatstronglysuggestthatouruniverseisthe product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. Although inflation is generically eternal into the future, it is not eternal into the past: it can be proven under reasonable assumptions that the inflating region must be incomplete in past directions, so some physics other than inflation is needed to describe the past boundary of the inflating region. PACS numbers: 98.80.cQ, 98.80.Bp, 98.80.Es 1. Introduction: the successes of inflation Since the proposal of the inflationary model some 25 years ago [1–4], inflation has been remarkably successful in explaining many important qualitative and quantitative properties of the universe. In this paper, I will summarize the key successes, and then discuss a number of issues associated with the eternal nature of inflation. -
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. -
Distinguished University Professor" at the University of Amsterdam Since 2005, Where He Has Held the Chair of Mathematical Physics Since 1992
Biography Robbert Dijkgraaf Robbert Dijkgraaf (born 1960) has been "Distinguished University Professor" at the University of Amsterdam since 2005, where he has held the chair of mathematical physics since 1992. Since 2008 he is President of the Royal Netherlands Academy of Arts and Sciences (KNAW). Robbert Dijkgraaf studied physics and mathematics at Utrecht University. After an interlude studying painting at Amsterdam's Gerrit Rietveld Academy, he gained his PhD cum laude in Utrecht in 1989. His supervisor was the Nobel Prize-winner Gerard 't Hooft. Robbert Dijkgraaf subsequently held positions at Princeton University and at Princeton's Institute for Advanced Study. His current focus is on string theory, quantum gravity, and the interface between mathematics and particle physics. His research was recognized in 2003 with the award of the NWO Spinoza Prize, the highest scientific award in the Netherlands. Robbert Dijkgraaf has been a visiting professor at universities including Harvard, MIT, Berkeley, and Kyoto. He is on the editorial boards of numerous scientific periodicals, and is also the scientific adviser to institutes in Cambridge, Bonn, Stanford, Dublin, and Paris. Since 2009 he is co-chair of the InterAcademy Council, a multinational organization of science academies, together with Professor Lu Yongxiang, President of the Chinese Academy of Sciences. Many of his activities are at the interface between science and society. His column in the NRC Handelsblad newspaper is intended for a broad public and deals with science, the arts, and other matters. A collection has been published in his book Blikwisselingen (Prometheus | Bert Bakker, 2008). Robbert Dijkgraaf is dedicated to bringing about greater public awareness of science, for example through his involvement with popular TV science programmes. -
Wall-Crossing, Free Fermions and Crystal Melting
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Springer - Publisher Connector Commun. Math. Phys. 301, 517–562 (2011) Communications in Digital Object Identifier (DOI) 10.1007/s00220-010-1153-1 Mathematical Physics Wall-Crossing, Free Fermions and Crystal Melting Piotr Sułkowski1,2, 1 California Institute of Technology, Pasadena, CA 91125, USA. E-mail: [email protected] 2 Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA Received: 15 December 2009 / Accepted: 10 June 2010 Published online: 26 October 2010 – © The Author(s) 2010. This article is published with open access at Springerlink.com Abstract: We describe wall-crossing for local, toric Calabi-Yaumanifolds without com- pact four-cycles, in terms of free fermions, vertex operators, and crystal melting. Firstly, to each such manifold we associate two states in the free fermion Hilbert space. The overlap of these states reproduces the BPS partition function corresponding to the non- commutative Donaldson-Thomas invariants, given by the modulus square of the topolog- ical string partition function. Secondly, we introduce the wall-crossing operators which represent crossing the walls of marginal stability associated to changes of the B-field through each two-cycle in the manifold. BPS partition functions in non-trivial chambers are given by the expectation values of these operators. Thirdly, we discuss crystal inter- pretation of such correlators for this whole class of manifolds. We describe evolution of these crystals upon a change of the moduli, and find crystal interpretation of the flop transition and the DT/PT transition. The crystals which we find generalize and unify various other Calabi-Yau crystal models which appeared in literature in recent years. -
Calabi-Yau Geometry and Higher Genus Mirror Symmetry
Calabi-Yau Geometry and Higher Genus Mirror Symmetry A dissertation presented by Si Li to The Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Mathematics Harvard University Cambridge, Massachusetts May 2011 © 2011 { Si Li All rights reserved. iii Dissertation Advisor: Professor Shing-Tung Yau Si Li Calabi-Yau Geometry and Higher Genus Mirror Symmetry Abstract We study closed string mirror symmetry on compact Calabi-Yau manifolds at higher genus. String theory predicts the existence of two sets of geometric invariants, from the A-model and the B-model on Calabi-Yau manifolds, each indexed by a non-negative inte- ger called genus. The A-model has been mathematically established at all genera by the Gromov-Witten theory, but little is known in mathematics for B-model beyond genus zero. We develop a mathematical theory of higher genus B-model from perturbative quantiza- tion techniques of gauge theory. The relevant gauge theory is the Kodaira-Spencer gauge theory, which is originally discovered by Bershadsky-Cecotti-Ooguri-Vafa as the closed string field theory of B-twisted topological string on Calabi-Yau three-folds. We generalize this to Calabi-Yau manifolds of arbitrary dimensions including also gravitational descen- dants, which we call BCOV theory. We give the geometric description of the perturbative quantization of BCOV theory in terms of deformation-obstruction theory. The vanishing of the relevant obstruction classes will enable us to construct the higher genus B-model. We carry out this construction on the elliptic curve and establish the corresponding higher genus B-model. -
2000 Annual Report
2001 ANNUAL REPORT ALFRED P. SLOAN FOUNDATION 1 CONTENTS 2001 Grants and Activities Science and Technology 5 Fellowships 5 Sloan Research Fellowships 5 Direct Support of Research 9 Neuroscience 9 Computational Molecular Biology 9 Limits to Knowledge 10 Marine Science 11 Other Science and Science Policy 15 History of Science and Technology 16 Standard of Living and Economic Performance 17 Industries 17 Industry Centers 17 Human Resources/Jobs/Income 21 Globalization 21 Business Organizations 22 Economics Research and Other Work 24 Nonprofit Sectors 26 Universities 26 Assessment of Government Performance 26 Work, Workforce and Working Families 30 Centers on Working Families 30 Workplace Structure and Opportunity 31 Working Families and Everyday Life 34 Education and Careers in Science and Technology 36 Scientific and Technical Careers 36 Anytime, Anyplace Learning 36 Professional Master’s Degrees 42 Information about Careers 47 Entry and Retention 48 Science and Engineering Education 48 Education for Minorities and Women 49 Minorities 49 Women 53 Public Understanding of Science and Technology 55 Books 55 Sloan Technology Book Series 57 Radio 58 2 Public Television 59 Commercial Television and Films 60 Theater 61 General 63 Selected National Issues and The Civic Program 64 Selected National Issues 64 September 11 64 Bioterrorism 66 Energy 68 Federal Statistics 69 Public Policy Research 69 The Civic Program 71 Additional Grants 73 2001 Financial Report Financial Review 75 Auditors’ Report 76 Balance Sheets 77 Statements of Activities 78 Statements of Cash Flows 79 Notes to Financial Statements 80 Schedules of Management and Investment Expenses 83 3 2001 GRANTS AND ACTIVITIES 4 SCIENCE AND TECHNOLOGY FELLOWSHIPS Sloan Research Fellowships $4,160,000 The Sloan Research Fellowship Program aims to stimulate fundamental research by young scholars with outstanding promise to contribute significantly to the advancement of knowledge. -
Is String Theory Holographic? 1 Introduction
Holography and large-N Dualities Is String Theory Holographic? Lukas Hahn 1 Introduction1 2 Classical Strings and Black Holes2 3 The Strominger-Vafa Construction3 3.1 AdS/CFT for the D1/D5 System......................3 3.2 The Instanton Moduli Space.........................6 3.3 The Elliptic Genus.............................. 10 1 Introduction The holographic principle [1] is based on the idea that there is a limit on information content of spacetime regions. For a given volume V bounded by an area A, the state of maximal entropy corresponds to the largest black hole that can fit inside V . This entropy bound is specified by the Bekenstein-Hawking entropy A S ≤ S = (1.1) BH 4G and the goings-on in the relevant spacetime region are encoded on "holographic screens". The aim of these notes is to discuss one of the many aspects of the question in the title, namely: "Is this feature of the holographic principle realized in string theory (and if so, how)?". In order to adress this question we start with an heuristic account of how string like objects are related to black holes and how to compare their entropies. This second section is exclusively based on [2] and will lead to a key insight, the need to consider BPS states, which allows for a more precise treatment. The most fully understood example is 1 a bound state of D-branes that appeared in the original article on the topic [3]. The third section is an attempt to review this construction from a point of view that highlights the role of AdS/CFT [4,5].