The Taiji Project for GWD in China & the Exploration of Unification Theory
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FIELDS MEDAL for Mathematical Efforts R
Recognizing the Real and the Potential: FIELDS MEDAL for Mathematical Efforts R Fields Medal recipients since inception Year Winners 1936 Lars Valerian Ahlfors (Harvard University) (April 18, 1907 – October 11, 1996) Jesse Douglas (Massachusetts Institute of Technology) (July 3, 1897 – September 7, 1965) 1950 Atle Selberg (Institute for Advanced Study, Princeton) (June 14, 1917 – August 6, 2007) 1954 Kunihiko Kodaira (Princeton University) (March 16, 1915 – July 26, 1997) 1962 John Willard Milnor (Princeton University) (born February 20, 1931) The Fields Medal 1966 Paul Joseph Cohen (Stanford University) (April 2, 1934 – March 23, 2007) Stephen Smale (University of California, Berkeley) (born July 15, 1930) is awarded 1970 Heisuke Hironaka (Harvard University) (born April 9, 1931) every four years 1974 David Bryant Mumford (Harvard University) (born June 11, 1937) 1978 Charles Louis Fefferman (Princeton University) (born April 18, 1949) on the occasion of the Daniel G. Quillen (Massachusetts Institute of Technology) (June 22, 1940 – April 30, 2011) International Congress 1982 William P. Thurston (Princeton University) (October 30, 1946 – August 21, 2012) Shing-Tung Yau (Institute for Advanced Study, Princeton) (born April 4, 1949) of Mathematicians 1986 Gerd Faltings (Princeton University) (born July 28, 1954) to recognize Michael Freedman (University of California, San Diego) (born April 21, 1951) 1990 Vaughan Jones (University of California, Berkeley) (born December 31, 1952) outstanding Edward Witten (Institute for Advanced Study, -
What's Inside
Newsletter A publication of the Controlled Release Society Volume 32 • Number 1 • 2015 What’s Inside 42nd CRS Annual Meeting & Exposition pH-Responsive Fluorescence Polymer Probe for Tumor pH Targeting In Situ-Gelling Hydrogels for Ophthalmic Drug Delivery Using a Microinjection Device Interview with Paolo Colombo Patent Watch Robert Langer Awarded the Queen Elizabeth Prize for Engineering Newsletter Charles Frey Vol. 32 • No. 1 • 2015 Editor Table of Contents From the Editor .................................................................................................................. 2 From the President ............................................................................................................ 3 Interview Steven Giannos An Interview with Paolo Colombo from University of Parma .............................................. 4 Editor 42nd CRS Annual Meeting & Exposition .......................................................................... 6 What’s on Board Access the Future of Delivery Science and Technology with Key CRS Resources .............. 9 Scientifically Speaking pH-Responsive Fluorescence Polymer Probe for Tumor pH Targeting ............................. 10 Arlene McDowell Editor In Situ-Gelling Hydrogels for Ophthalmic Drug Delivery Using a Microinjection Device ........................................................................................................ 12 Patent Watch ................................................................................................................... 14 Special -
Advances in Theoretical & Computational Physics
ISSN: 2639-0108 Research Article Advances in Theoretical & Computational Physics Supreme Theory of Everything Ulaanbaatar Tarzad *Corresponding author Ulaanbaatar Tarzad, Department of Physics, School of Applied Sciences, Department of Physics, School of Applied Sciences, Mongolian Mongolian University of Science and Technology, Ulaanbaatar, Mongolia, University of Science and Technology E-mail: [email protected] Submitted: 27 Mar 2019; Accepted: 24 Apr 2019; Published: 06 June 2019 Abstract Not only universe, but everything has general characters as eternal, infinite, cyclic and wave-particle duality. Everything from elementary particles to celestial bodies, from electromagnetic wave to gravity is in eternal motions, which dissects only to circle. Since everything is described only by trigonometry. Without trigonometry and mathematical circle, the science cannot indicate all the beauty of harmonic universe. Other method may be very good, but it is not perfect. Some part is very nice, another part is problematic. General Theory of Relativity holds that gravity is geometric. Quantum Mechanics describes all particles by wave function of trigonometry. In this paper using trigonometry, particularly mathematics circle, a possible version of the unification of partial theories, evolution history and structure of expanding universe, and the parallel universes are shown. Keywords: HRD, Trigonometry, Projection of Circle, Singularity, The reality of universe describes by geometry, because of that not Celestial Body, Black Hole and Parallel Universes. only gravity is geometrical, but everything is it and nothing is linear. One of the important branches of geometry is trigonometry dealing Introduction with circle and triangle. For this reason, it is easier to describe nature Today scientists describe the universe in terms of two basic partial of universe by mathematics circle. -
Some Comments on Physical Mathematics
Preprint typeset in JHEP style - HYPER VERSION Some Comments on Physical Mathematics Gregory W. Moore Abstract: These are some thoughts that accompany a talk delivered at the APS Savannah meeting, April 5, 2014. I have serious doubts about whether I deserve to be awarded the 2014 Heineman Prize. Nevertheless, I thank the APS and the selection committee for their recognition of the work I have been involved in, as well as the Heineman Foundation for its continued support of Mathematical Physics. Above all, I thank my many excellent collaborators and teachers for making possible my participation in some very rewarding scientific research. 1 I have been asked to give a talk in this prize session, and so I will use the occasion to say a few words about Mathematical Physics, and its relation to the sub-discipline of Physical Mathematics. I will also comment on how some of the work mentioned in the citation illuminates this emergent field. I will begin by framing the remarks in a much broader historical and philosophical context. I hasten to add that I am neither a historian nor a philosopher of science, as will become immediately obvious to any expert, but my impression is that if we look back to the modern era of science then major figures such as Galileo, Kepler, Leibniz, and New- ton were neither physicists nor mathematicans. Rather they were Natural Philosophers. Even around the turn of the 19th century the same could still be said of Bernoulli, Euler, Lagrange, and Hamilton. But a real divide between Mathematics and Physics began to open up in the 19th century. -
Tao Awarded Nemmers Prize
Tao Awarded Nemmers Prize Northwestern University has announced that numerous other awards, including the Terence Chi-Shen Tao has received the 2010 Salem Prize (2000), the Bôcher Prize Frederic Esser Nemmers Prize in Mathematics, be- (2002), the Clay Research Award of the lieved to be one of the largest monetary awards in Clay Mathematics Institute (2003), the mathematics in the United States, for outstanding SASTRA Ramanujan Prize (2006), the achievements in the discipline. Awarded to schol- Ostrowski Prize (2007), the Waterman ars who made major contributions to new knowl- Award (2008), and the King Faisal Prize edge or to the development of significant new (cowinner, 2010). He is a Fellow of the modes of analysis, the prize carries a US$175,000 Royal Society, the Australian Academy stipend. of Sciences (corresponding member), Tao, a professor of mathematics at University the U.S. National Academy of Sciences of California, Los Angeles, was honored “for math- (foreign member), and the American ematics of astonishing breadth, depth and original- Academy of Arts and Sciences. ity”. In connection with the award, Tao will deliver Tao’s research interests include Terence Tao public lectures and participate in other scholarly harmonic analysis, partial dif- activities at Northwestern during the 2010–2011 ferential equations, combinatorics, and num- and 2011–2012 academic years. ber theory. He is an associate editor of the Tao, who has been dubbed the “Mozart of American Journal of Mathematics (2002–) and Math”, was born in Adelaide, Australia, in 1975. of Dynamics of Partial Differential Equations He started to learn calculus when he was seven (2003–) and an editor of the Journal of the Ameri- years old. -
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]. -
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. -
The Discovery of Asymptotic Freedom
The Discovery of Asymptotic Freedom The 2004 Nobel Prize in Physics, awarded to David Gross, Frank Wilczek, and David Politzer, recognizes the key discovery that explained how quarks, the elementary constituents of the atomic nucleus, are bound together to form protons and neutrons. In 1973, Gross and Wilczek, working at Princeton, and Politzer, working independently at Harvard, showed that the attraction between quarks grows weaker as the quarks approach one another more closely, and correspondingly that the attraction grows stronger as the quarks are separated. This discovery, known as “asymptotic freedom,” established quantum chromodynamics (QCD) as the correct theory of the strong nuclear force, one of the four fundamental forces in Nature. At the time of the discovery, Wilczek was a 21-year-old graduate student working under Gross’s supervision at Princeton, while Politzer was a 23-year-old graduate student at Harvard. Currently Gross is the Director of the Kavli Institute for Theoretical Physics at the University of California at Santa Barbara, and Wilczek is the Herman Feshbach Professor of Physics at MIT. Politzer is Professor of Theoretical Physics at Caltech; he joined the Caltech faculty in 1976. Of the four fundamental forces --- the others besides the strong nuclear force are electromagnetism, the weak nuclear force (responsible for the decay of radioactive nuclei), and gravitation --- the strong force was by far the most poorly understood in the early 1970s. It had been suggested in 1964 by Caltech physicist Murray Gell-Mann that protons and neutrons contain more elementary objects, which he called quarks. Yet isolated quarks are never seen, indicating that the quarks are permanently bound together by powerful nuclear forces. -
Superstring Theory Volume 2: Loop Amplitudes, Anomalies and Phenomenology 25Th Anniversary Edition
Cambridge University Press 978-1-107-02913-2 - Superstring Theory: Volume 2: Loop Amplitudes, Anomalies and Phenomenology: 25th Anniversary Edition Michael B. Green, John H. Schwarz and Edward Witten Frontmatter More information Superstring Theory Volume 2: Loop Amplitudes, Anomalies and Phenomenology 25th Anniversary Edition Twenty-five years ago, Michel Green, John Schwarz, and Edward Witten wrote two volumes on string theory. Published during a period of rapid progress in this subject, these volumes were highly influential for a generation of students and researchers. Despite the immense progress that has been made in the field since then, the systematic exposition of the foundations of superstring theory presented in these volumes is just as relevant today as when first published. Volume 2 is concerned with the evaluation of one-loop amplitudes, the study of anomalies, and phenomenology. It examines the low energy effective field theory analysis of anomalies, the emergence of the gauge groups E8 × E8 and SO(32), and the four-dimensional physics that arises by compactification of six extra dimensions. Featuring a new Preface setting the work in context in light of recent advances, this book is invaluable for graduate students and researchers in high energy physics and astrophysics, as well as for mathematicians. MICHAEL B. GREEN is the Lucasian Professor of Mathematics at the University of Cambridge, JOHN H. SCHWARZ is the Harold Brown Professor of Theoretical Physics at the California Institute of Technology, and EDWARD WITTEN is the Charles Simonyi Professor of Mathematical Physics at the Institute for Advanced Study. Each of them has received numerous honors and awards. -
The Top Mathematics Award
Fields told me and which I later verified in Sweden, namely, that Nobel hated the mathematician Mittag- Leffler and that mathematics would not be one of the do- mains in which the Nobel prizes would The Top Mathematics be available." Award Whatever the reason, Nobel had lit- tle esteem for mathematics. He was Florin Diacuy a practical man who ignored basic re- search. He never understood its impor- tance and long term consequences. But Fields did, and he meant to do his best John Charles Fields to promote it. Fields was born in Hamilton, Ontario in 1863. At the age of 21, he graduated from the University of Toronto Fields Medal with a B.A. in mathematics. Three years later, he fin- ished his Ph.D. at Johns Hopkins University and was then There is no Nobel Prize for mathematics. Its top award, appointed professor at Allegheny College in Pennsylvania, the Fields Medal, bears the name of a Canadian. where he taught from 1889 to 1892. But soon his dream In 1896, the Swedish inventor Al- of pursuing research faded away. North America was not fred Nobel died rich and famous. His ready to fund novel ideas in science. Then, an opportunity will provided for the establishment of to leave for Europe arose. a prize fund. Starting in 1901 the For the next 10 years, Fields studied in Paris and Berlin annual interest was awarded yearly with some of the best mathematicians of his time. Af- for the most important contributions ter feeling accomplished, he returned home|his country to physics, chemistry, physiology or needed him. -
Alex Flournoy, 303-273-3712, [email protected] Project Title
Physics Department Senior Design Project Proposal Project Mentor: Alex Flournoy, 303-273-3712, [email protected] (Name, phone, email) Project Title: The AdS/CFT correspondence – A Tool from String Theory Project Type: [ ] Team; Number of students__1___ [ X] Honors Objective (What is the science and/or engineering in this project?) The AdS/CFT correspondence is perhaps one of the most useful results to arise from String Theory since its discovery. Questions about the role of String Theory as a “fundamental theory” aside, this particular result, relating calculations in non-gravitational field theory to purely gravitational calculations, promises to bridge the fields of high-energy/gravitational and condensed-matter physics in an unprecedented manner. It is the opinion of many in the field that this result serves as the basis for the future of research in String Theory as a “tool” for computation. A student who can grasp even the basic notions behind this correspondence will be in an advantageous position to enter particle/gravitational/condensed-matter studies/research with a unique and powerful perspective. Of course a proper understanding of this result requires an extensive background in advanced general relativity, particle physics, string theory and the mathematics of conformal field theory. This can render the correspondence a prohibitive tool to consider for even for expert theorists if they do not have a broad enough background. A clean presentation of the correspondence that would be suitable for implementation by theorists without the full background is lacking. Constructing such a presentation and a “manual” for the use of the tool is the chief goal of this senior design project. -
Black Holes and Quark Confinement
SPECIAL SECTION: Black holes and quark confinement Edward Witten Department of Physics, Cal Tech, Pasadena, CA and CIT-USC Center For Theoretical Physics, USC, Los Angeles CA, USA Present address: Institute for Advanced Study, Princeton, NJ 08540, USA MOST expositions of string theory focus on its possible large loop C in space–time (Figure 2). Let A(C) be the use as a framework for unifying the forces of nature. area of a soap bubble of minimal area whose boundary But I will take a different tack in this article. Rather is C. Quark confinement occurs if the probability ampli- than the unification of the forces, I will here describe tude W(C) for a quark to propagate around the loop C is what one might call the unification of the ideas. exponentially small when the area is large, Let us begin with the classic and not fully solved problem of ‘quark confinement’. From a variety of ex- W(C) ~ exp(–kA(C)) periments, physicists learned roughly 30 years ago that protons, neutrons, pions, and other strongly interacting with some k > 0. particles are made from quarks (and antiquarks, and In this form, the hypothesis of quark confinement has gluons). But we never see an isolated quark. been tested extensively in computer simulations since It is believed that if one tries to separate a quark– the late 1970s. And this, together with ordinary experi- antiquark pair in, say, a pion, the energy required grows ments, gives confidence that it is correct. But we still do linearly with the distance between the quark and anti- not fully understand it.