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TWAS Fellowships Worldwide
CDC Round Table, ICTP April 2016 With science and engineering, countries can address challenges in agriculture, climate, health TWAS’s and energy. guiding principles 2 Food security Challenges Water quality for a Energy security new era Biodiversity loss Infectious diseases Climate change 3 A Globally, 81 nations fall troubling into the category of S&T- gap lagging countries. 48 are classified as Least Developed Countries. 4 The role of TWAS The day-to-day work of TWAS is focused in two critical areas: •Improving research infrastructure •Building a corps of PhD scholars 5 TWAS Research Grants 2,202 grants awarded to individuals and research groups (1986-2015) 6 TWAS’ AIM: to train 1000 PhD students by 2017 Training PhD-level scientists: •Researchers and university-level educators •Future leaders for science policy, business and international cooperation Rapidly growing opportunities P BRAZIL A K I N D I CA I RI A S AF TH T SOU A N M KENYA EX ICO C H I MALAYSIA N A IRAN THAILAND TWAS Fellowships Worldwide NRF, South Africa - newly on board 650+ fellowships per year PhD fellowships +460 Postdoctoral fellowships +150 Visiting researchers/professors + 45 17 Programme Partners BRAZIL: CNPq - National Council MALAYSIA: UPM – Universiti for Scientific and Technological Putra Malaysia WorldwideDevelopment CHINA: CAS - Chinese Academy of KENYA: icipe – International Sciences Centre for Insect Physiology and Ecology INDIA: CSIR - Council of Scientific MEXICO: CONACYT– National & Industrial Research Council on Science and Technology PAKISTAN: CEMB – National INDIA: DBT - Department of Centre of Excellence in Molecular Biotechnology Biology PAKISTAN: ICCBS – International Centre for Chemical and INDIA: IACS - Indian Association Biological Sciences for the Cultivation of Science PAKISTAN: CIIT – COMSATS Institute of Information INDIA: S.N. -
Numerical Computation with Rational Functions
NUMERICAL COMPUTATION WITH RATIONAL FUNCTIONS (scalars only) Nick Trefethen, University of Oxford and ENS Lyon + thanks to Silviu Filip, Abi Gopal, Stefan Güttel, Yuji Nakatsukasa, and Olivier Sète 1/26 1. Polynomial vs. rational approximations 2. Four representations of rational functions 2a. Quotient of polynomials 2b. Partial fractions 2c. Quotient of partial fractions (= barycentric) 2d. Transfer function/matrix pencil 3. The AAA algorithm with Nakatsukasa and Sète, to appear in SISC 4. Application: conformal maps with Gopal, submitted to Numer. Math. 5. Application: minimax approximation with Filip, Nakatsukasa, and Beckermann, to appear in SISC 6. Accuracy and noise 2/26 1. Polynomial vs. rational approximation Newman, 1964: approximation of |x| on [−1,1] −휋 푛 퐸푛0 ~ 0.2801. ./푛 , 퐸푛푛 ~ 8푒 Poles and zeros of r: exponentially clustered near x=0, exponentially diminishing residues. Rational approximation is nonlinear, so algorithms are nontrivial. poles There may be nonuniqueness and local minima. type (20,20) 3/26 2. Four representations of rational functions Alpert, Carpenter, Coelho, Gonnet, Greengard, Hagstrom, Koerner, Levy, Quotient of polynomials 푝(푧)/푞(푧) SK, IRF, AGH, ratdisk Pachón, Phillips, Ruttan, Sanathanen, Silantyev, Silveira, Varga, White,… 푎푘 Beylkin, Deschrijver, Dhaene, Drmač, Partial fractions 푧 − 푧 VF, exponential sums Greengard, Gustavsen, Hochman, 푘 Mohlenkamp, Monzón, Semlyen,… Berrut, Filip, Floater, Gopal, Quotient of partial fractions 푛(푧)/푑(푧) Floater-Hormann, AAA Hochman, Hormann, Ionita, Klein, Mittelmann, Nakatsukasa, Salzer, (= barycentric) Schneider, Sète, Trefethen, Werner,… 푇 −1 Antoulas, Beattie, Beckermann, Berljafa, Transfer function/matrix pencil 푐 푧퐵 − 퐴 푏 IRKA, Loewner, RKFIT Druskin, Elsworth, Gugercin, Güttel, Knizhnerman, Meerbergen, Ruhe,… Sometimes the boundaries are blurry! 4/26 2a. -
Millennium Prize for the Poincaré
FOR IMMEDIATE RELEASE • March 18, 2010 Press contact: James Carlson: [email protected]; 617-852-7490 See also the Clay Mathematics Institute website: • The Poincaré conjecture and Dr. Perelmanʼs work: http://www.claymath.org/poincare • The Millennium Prizes: http://www.claymath.org/millennium/ • Full text: http://www.claymath.org/poincare/millenniumprize.pdf First Clay Mathematics Institute Millennium Prize Announced Today Prize for Resolution of the Poincaré Conjecture a Awarded to Dr. Grigoriy Perelman The Clay Mathematics Institute (CMI) announces today that Dr. Grigoriy Perelman of St. Petersburg, Russia, is the recipient of the Millennium Prize for resolution of the Poincaré conjecture. The citation for the award reads: The Clay Mathematics Institute hereby awards the Millennium Prize for resolution of the Poincaré conjecture to Grigoriy Perelman. The Poincaré conjecture is one of the seven Millennium Prize Problems established by CMI in 2000. The Prizes were conceived to record some of the most difficult problems with which mathematicians were grappling at the turn of the second millennium; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; to emphasize the importance of working towards a solution of the deepest, most difficult problems; and to recognize achievement in mathematics of historical magnitude. The award of the Millennium Prize to Dr. Perelman was made in accord with their governing rules: recommendation first by a Special Advisory Committee (Simon Donaldson, David Gabai, Mikhail Gromov, Terence Tao, and Andrew Wiles), then by the CMI Scientific Advisory Board (James Carlson, Simon Donaldson, Gregory Margulis, Richard Melrose, Yum-Tong Siu, and Andrew Wiles), with final decision by the Board of Directors (Landon T. -
Economic Perspectives
The Journal of The Journal of Economic Perspectives Economic Perspectives The Journal of Fall 2016, Volume 30, Number 4 Economic Perspectives Symposia Immigration and Labor Markets Giovanni Peri, “Immigrants, Productivity, and Labor Markets” Christian Dustmann, Uta Schönberg, and Jan Stuhler, “The Impact of Immigration: Why Do Studies Reach Such Different Results?” Gordon Hanson and Craig McIntosh, “Is the Mediterranean the New Rio Grande? US and EU Immigration Pressures in the Long Run” Sari Pekkala Kerr, William Kerr, Çag˘lar Özden, and Christopher Parsons, “Global Talent Flows” A journal of the American Economic Association What is Happening in Game Theory? Larry Samuelson, “Game Theory in Economics and Beyond” Vincent P. Crawford, “New Directions for Modelling Strategic Behavior: 30, Number 4 Fall 2016 Volume Game-Theoretic Models of Communication, Coordination, and Cooperation in Economic Relationships” Drew Fudenberg and David K. Levine, “Whither Game Theory? Towards a Theory of Learning in Games” Articles Dave Donaldson and Adam Storeygard, “The View from Above: Applications of Satellite Data in Economics” Robert M. Townsend, “Village and Larger Economies: The Theory and Measurement of the Townsend Thai Project” Amanda Bayer and Cecilia Elena Rouse, “Diversity in the Economics Profession: A New Attack on an Old Problem” Recommendations for Further Reading Fall 2016 The American Economic Association The Journal of Correspondence relating to advertising, busi- Founded in 1885 ness matters, permission to quote, or change Economic Perspectives of address should be sent to the AEA business EXECUTIVE COMMITTEE office: [email protected]. Street ad- dress: American Economic Association, 2014 Elected Officers and Members A journal of the American Economic Association Broadway, Suite 305, Nashville, TN 37203. -
An Extension of Matlab to Continuous Functions and Operators∗
SIAM J. SCI. COMPUT. c 2004 Society for Industrial and Applied Mathematics Vol. 25, No. 5, pp. 1743–1770 AN EXTENSION OF MATLAB TO CONTINUOUS FUNCTIONS AND OPERATORS∗ † † ZACHARY BATTLES AND LLOYD N. TREFETHEN Abstract. An object-oriented MATLAB system is described for performing numerical linear algebra on continuous functions and operators rather than the usual discrete vectors and matrices. About eighty MATLAB functions from plot and sum to svd and cond have been overloaded so that one can work with our “chebfun” objects using almost exactly the usual MATLAB syntax. All functions live on [−1, 1] and are represented by values at sufficiently many Chebyshev points for the polynomial interpolant to be accurate to close to machine precision. Each of our overloaded operations raises questions about the proper generalization of familiar notions to the continuous context and about appropriate methods of interpolation, differentiation, integration, zerofinding, or transforms. Applications in approximation theory and numerical analysis are explored, and possible extensions for more substantial problems of scientific computing are mentioned. Key words. MATLAB, Chebyshev points, interpolation, barycentric formula, spectral methods, FFT AMS subject classifications. 41-04, 65D05 DOI. 10.1137/S1064827503430126 1. Introduction. Numerical linear algebra and functional analysis are two faces of the same subject, the study of linear mappings from one vector space to another. But it could not be said that mathematicians have settled on a language and notation that blend the discrete and continuous worlds gracefully. Numerical analysts favor a concrete, basis-dependent matrix-vector notation that may be quite foreign to the functional analysts. Sometimes the difference may seem very minor between, say, ex- pressing an inner product as (u, v)orasuTv. -
A View from the Bridge Natalie Paquette
INFERENCE / Vol. 3, No. 4 A View from the Bridge Natalie Paquette tring theory is a quantum theory of gravity.1 Albert example, supersymmetric theories require particles to Einstein’s theory of general relativity emerges natu- come in pairs. For every bosonic particle there is a fermi- rally from its equations.2 The result is consistent in onic superpartner. Sthe sense that its calculations do not diverge to infinity. Supersymmetric field theory has a disheartening String theory may well be the only consistent quantum impediment. Suppose that a supersymmetric quantum theory of gravity. If true, this would be a considerable field theory is defined on a generic curved manifold. The virtue. Whether it is true or not, string theory is indis- Euclidean metric of Newtonian physics and the Lorentz putably the source of profound ideas in mathematics.3 metric of special relativity are replaced by the manifold’s This is distinctly odd. A line of influence has always run own metric. Supercharges correspond to conserved Killing from mathematics to physics. When Einstein struggled spinors. Solutions to the Killing spinor equations are plen- to express general relativity, he found the tools that he tiful in a flat space, but the equations become extremely needed had been created sixty years before by Bernhard restrictive on curved manifolds. They are so restrictive Riemann. The example is typical. Mathematicians discov- that they have, in general, no solutions. Promoting a flat ered group theory long before physicists began using it. In supersymmetric field theory to a generic curved mani- the case of string theory, it is often the other way around. -
Stability of Tangent Bundles of Complete Intersections and Effective
STABILITY OF TANGENT BUNDLES OF COMPLETE INTERSECTIONS AND EFFECTIVE RESTRICTION JIE LIU ABSTRACT. For n ≥ 3, let M be an (n + r)-dimensional irreducible Hermitian symmetric space of compact type and let OM(1) be the ample generator of Pic(M). Let Y = H1 ∩···∩ Hr be a smooth complete intersection of dimension n where Hi ∈ |OM(di)| with di ≥ 2. We prove a vanishing theorem for twisted holomor- phic forms on Y. As an application, we show that the tangent bundle TY of Y is stable. Moreover, if X is a smooth hypersurface of degree d in Y such that the restriction Pic(Y) → Pic(X) is surjective, we establish some effective results for d to guarantee the stability of the restriction TY|X. In particular, if Y is a general n+1 hypersurface in P and X is general smooth divisor in Y, we show that TY|X is stable except for some well-known examples. We also address the cases where the Picard group increases by restriction. CONTENTS 1. Introduction 1 2. Hermitian symmetric spaces and Lefschetz properties 5 3. Twisted (n − 1)-forms and special cohomologies 7 4. Extension of twisted vector fields 10 5. Stability and effective restriction with invariant Picard group 14 6. Hyperplane of cubic threefolds 20 Reference 25 1. INTRODUCTION arXiv:1711.03413v3 [math.AG] 22 Oct 2018 It has been one of main problems in K¨ahler geometry to study which Fano manifolds with b2 = 1 admit a K¨ahler-Einstein metric. The celebrated Yau-Tian- Donaldson conjecture asserts that a Fano manifold admits a K¨ahler-Einstein met- ric if and only if it is K-polystable. -
Householder Triangularization of a Quasimatrix
IMA Journal of Numerical Analysis (2010) 30, 887–897 doi:10.1093/imanum/drp018 Advance Access publication on August 21, 2009 Householder triangularization of a quasimatrix LLOYD N.TREFETHEN† Oxford University Computing Laboratory, Wolfson Building, Parks Road, Downloaded from Oxford OX1 3QD, UK [Received on 4 July 2008] A standard algorithm for computing the QR factorization of a matrix A is Householder triangulariza- tion. Here this idea is generalized to the situation in which A is a quasimatrix, that is, a ‘matrix’ whose http://imajna.oxfordjournals.org/ ‘columns’ are functions defined on an intervala [ , b]. Applications are mentioned to quasimatrix least squares fitting, singular value decomposition and determination of ranks, norms and condition numbers, and numerical illustrations are presented using the chebfun system. Keywords: Householder triangularization; QR factorization; chebfun; quasimatrix; singular value decom- position. 1. QR factorization and Householder triangularization at Radcliffe Science Library, Bodleian Library on April 18, 2012 Let A be an m n matrix, where m n. A (reduced) QR factorization of A is a factorization × > x x x x q q q q r r r r x x x x q q q q r r r A QR, x x x x q q q q r r , (1.1) = x x x x q q q q r x x x x q q q q x x x x q q q q where Q is m n with orthonormal columns and R is upper triangular. Here and in subsequent equations we illustrate our× matrix operations by schematic pictures in which x denotes an arbitrary entry, r denotes an entry of an upper triangular matrix, q denotes an entry of an orthonormal column and a blank denotes a zero. -
Meetings & Conferences of The
Meetings & Conferences of the AMS IMPORTANT INFORMATION REGARDING MEETINGS PROGRAMS: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links to the abstract for each talk can be found on the AMS website. See www.ams.org/meetings/. Final programs for Sectional Meetings will be archived on the AMS website accessible from the stated URL . Jill Pipher, Brown University, Harmonic analysis and New Brunswick, New elliptic boundary value problems. David Vogan, Department of Mathematics, MIT, Matri- Jersey ces almost of order two. Wei Zhang, Columbia University, The Euler product and Rutgers University the Taylor expansion of an L-function. November 14–15, 2015 Special Sessions Saturday – Sunday If you are volunteering to speak in a Special Session, you Meeting #1115 should send your abstract as early as possible via the ab- Eastern Section stract submission form found at www.ams.org/cgi-bin/ Associate secretary: Steven H. Weintraub abstracts/abstract.pl. Announcement issue of Notices: September 2015 Advances in Valuation Theory, Samar El Hitti, New York Program first available on AMS website: October 1, 2015 City College of Technology, City University of New York, Issue of Abstracts: Volume 36, Issue 4 Franz-Viktor Kuhlmann, University of Saskatchewan, and Deadlines Hans Schoutens, New York City College of Technology, For organizers: Expired City University of New York. For abstracts: Expired Algebraic Geometry and Combinatorics, Elizabeth Drel- lich, University of North Texas, Erik Insko, Florida Gulf The scientific information listed below may be dated. Coast University, Aba Mbirika, University of Wisconsin- For the latest information, see www.ams.org/amsmtgs/ Eau Claire, and Heather Russell, Washington College. -
Breakthrough Prize in Mathematics Awarded to Terry Tao
156 Breakthrough Prize in Mathematics awarded to Terry Tao Our congratulations to Australian Mathematician Terry Tao, one of five inaugu- ral winners of the Breakthrough Prizes in Mathematics, announced on 23 June. Terry is based at the University of California, Los Angeles, and has been awarded the prize for numerous breakthrough contributions to harmonic analysis, combi- natorics, partial differential equations and analytic number theory. The Breakthrough Prize in Mathematics was launched by Mark Zuckerberg and Yuri Milner at the Breakthrough Prize ceremony in December 2013. The other winners are Simon Donaldson, Maxim Kontsevich, Jacob Lurie and Richard Tay- lor. All five recipients of the Prize have agreed to serve on the Selection Committee, responsible for choosing subsequent winners from a pool of candidates nominated in an online process which is open to the public. From 2015 onwards, one Break- through Prize in Mathematics will be awarded every year. The Breakthrough Prizes honor important, primarily recent, achievements in the categories of Fundamental Physics, Life Sciences and Mathematics. The prizes were founded by Sergey Brin and Anne Wojcicki, Mark Zuckerberg and Priscilla Chan, and Yuri and Julia Milner, and aim to celebrate scientists and generate excitement about the pursuit of science as a career. Laureates will receive their trophies and $3 million each in prize money at a televised award ceremony in November, designed to celebrate their achievements and inspire the next genera- tion of scientists. As part of the ceremony schedule, they also engage in a program of lectures and discussions. See https://breakthroughprize.org and http://www.nytimes.com/2014/06/23/us/ the-multimillion-dollar-minds-of-5-mathematical-masters.html? r=1 for further in- formation.. -
Publications by Lloyd N. Trefethen
Publications by Lloyd N. Trefethen I. Books I.1. Numerical Conformal Mapping, editor, 269 pages. Elsevier, 1986. I.2. Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, x+315 pages. Graduate textbook, privately published at http://comlab.ox.ac.uk/nick.trefethen/, 1996. I.3. Numerical Linear Algebra, with David Bau III, xii+361 pages. SIAM, 1997. I.4. Spectral Methods in MATLAB, xviii+165 pages. SIAM, 2000. I.5. Schwarz-Christoffel Mapping, with Tobin A. Driscoll, xvi+132 pages. Cambridge U. Press, 2002. I.6. Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators, with Mark Embree, xviii+606 pages. Princeton U. Press, 2005. I.7. Trefethen’s Index Cards: Forty years of Notes about People, Words, and Mathematics, xv + 368 pages. World Scientific Publishing, 2011. I.8. Approximation Theory and Approximation Practice. SIAM, to appear in 2013. In addition to these a book has been published by other authors about the international problem solving challenge I organised in 2002 (item VIII.8 below): F. Bornemann, D. Laurie, S. Wagon and D. Waldvogel, The SIAM 100-Digit Challenge, SIAM, 2004, to appear in German translation as Abenteuer Numerik: Eine Führung entlang der Herausforderung von Trefethen, Springer, 2006. II. Finite difference and spectral methods for partial differential equations II.1. Group velocity in finite difference schemes. SIAM Review 24 (1982), 113-136. II.2. Group velocity interpretation of the stability theory of Gustafsson, Kreiss, and Sundström. J. Comp. Phys. 49 (1983), 199-217. II.3. On Lp-instability and dispersion at discontinuities in finite difference schemes. -
First Combined British Mathematical Colloquium and British Applied
First combined British Mathematical Colloquium and British Applied Mathematics Colloquium (54th British Mathematical Colloquium and incorporating the 44th British Theoretical Mechanics Colloquium) University of Warwick, 7th–12th April 2002 Programme Monday 8th April Plenary speakers Joan Birman (Columbia), Peter Sarnak (Princeton) Morning speakers Garth Dales (Leeds), Keith Ball (UCL) Day-long special session on Braids and Low-Dimensional Topology Daan Krammer (Basel), John Crisp (Bourgogne), Patrick Dehornoy (Caen), Peter Teichner (San Diego – to be confirmed) Day-long special session on Number Theory Detta Dickinson (York), Rob de Jeu (Durham), Jens Marklof (Bristol), Anton Deitmar (Exeter) Evening BMC AGM and discussion on education Tuesday 9th April Plenary speakers Sandy Green (Oxford and Warwick), Ingrid Daubechies (Princeton) Morning speakers Jeremy Gray (Open), Jackie Stedall (Oxford), Ulrike Tillmann (Oxford), Maxim Kazar- ian (Moscow) Day-long special session on Representation Theory Andrei Zelevinsky (Northeastern), G Hiss (Aachen), RT Curtis (Birmingham), W Crawley-Boevey (Leeds) Evening CUP/Springer reception Splinter groups (Monday and Tuesday afternoons) see the back of this form Wednesday 10th April Plenary speakers Persi Diaconis (Stanford), Richard Karp (Berkeley), David Mumford (Brown) Morning discussion sessions Dynamical systems led by Steve Wiggins (Bristol) and Kostya Khanin (Newton/Heriot Watt) Discrete mathematics led by Bela Bollobas (Memphis) and Mark Dyer (Leeds) Afternoon discussion sessions Quantum phenomena