Part 1. Prelude to Topology
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Dedicated to Lou Kauffman for His 70Th Birthday 1. Knot Theory
Dedicated to Lou Kauffman for his 70th birthday KNOT THEORY: FROM FOX 3-COLORINGS OF LINKS TO YANG-BAXTER HOMOLOGY AND KHOVANOV HOMOLOGY JOZEF´ H. PRZYTYCKI Abstract: This paper is an extended account of my “Introductory Plenary talk at Knots in Hellas 2016” conference1. We start from the short introduction to Knot Theory from the historical perspective, starting from Heraclas text (the first century AD), mentioning R.Llull (1232-1315), A.Kircher (1602-1680), Leibniz idea of Geometria Situs (1679), and J.B.Listing (student of Gauss) work of 1847. We spend some space on Ralph H. Fox (1913-1973) elementary introduction to diagram colorings (1956). In the second section we describe how Fox work was generalized to distributive colorings (racks and quandles) and eventually in the work of Jones and Turaev to link invariants via Yang-Baxter operators; here the importance of statistical mechanics to topology will be mentioned. Finally we describe recent developments which started with Mikhail Khovanov work on categorification of the Jones polynomial. By analogy to Khovanov homology we build homology of distributive structures (including homology of Fox colorings) and generalize it to homology of Yang-Baxter operators. We speculate, with supporting evidence, on co-cycle invariants of knots coming from Yang-Baxter homology. Here the work of Fenn-Rourke-Sanderson (geometric realization of pre-cubic sets of link diagrams) and Carter-Kamada-Saito (co-cycle invariants of links) will be discussed and ex- panded. No deep knowledge of Knot Theory, homological algebra, or statistical mechanics is assumed as we work from basic principles. Because of this, some topics will be only briefly described. -
Campus Profile Sept 2018.Indd
CAMPUS PROFILE AND POINTS OF DISTINCTION campus profileOCTOBER 2018 CAMPUS PROFILE AND POINTS OF DISTINCTION At the University of California San Diego, we constantly push boundaries and challenge expectations. Established in 1960, UC San Diego has been shaped by exceptional scholars who aren’t afraid to take risks and redefine conventional wisdom. Today, as one of the top 15 research universities in the world, we are driving innovation and change to advance society, propel economic growth, and make our world a better place. UC San Diego’s main campus is located near the Pacific Ocean on 1,200 acres of coastal woodland in La Jolla, California. The campus sits on land formerly inhabited by Kumeyaay tribal members, the original native inhabitants of San Diego County. UC San Diego’s rich academic portfolio includes six undergraduate colleges, five academic divisions, and five graduate and professional schools. BY THE NUMBERS • 36,624 Total campus enrollment (as of Fall 2017); • 16 Number of Nobel laureates who have taught the largest number of students among colleges on campus and universities in San Diego County. • 201 Memberships held by current and emeriti • 97,670 Total freshman applications for 2018 faculty in the National Academy of Sciences (73), National Academy of Engineering (84), • 4.13 Admitted freshman average high school GPA and National Academy of Medicine (44). • $4.7 billion Fiscal year 2016-17 revenues; • 4 Scripps Institution of Oceanography operates 20 percent of this total is revenue from contracts three research vessels and an innovative Floating and grants, most of which is from the federal Instrument Platform (FLIP), enabling faculty, government for research. -
Transnational Mathematics and Movements: Shiing- Shen Chern, Hua Luogeng, and the Princeton Institute for Advanced Study from World War II to the Cold War1
Chinese Annals of History of Science and Technology 3 (2), 118–165 (2019) doi: 10.3724/SP.J.1461.2019.02118 Transnational Mathematics and Movements: Shiing- shen Chern, Hua Luogeng, and the Princeton Institute for Advanced Study from World War II to the Cold War1 Zuoyue Wang 王作跃,2 Guo Jinhai 郭金海3 (California State Polytechnic University, Pomona 91768, US; Institute for the History of Natural Sciences, Chinese Academy of Sciences, Beijing 100190, China) Abstract: This paper reconstructs, based on American and Chinese primary sources, the visits of Chinese mathematicians Shiing-shen Chern 陈省身 (Chen Xingshen) and Hua Luogeng 华罗庚 (Loo-Keng Hua)4 to the Institute for Advanced Study in Princeton in the United States in the 1940s, especially their interactions with Oswald Veblen and Hermann Weyl, two leading mathematicians at the IAS. It argues that Chern’s and Hua’s motivations and choices in regard to their transnational movements between China and the US were more nuanced and multifaceted than what is presented in existing accounts, and that socio-political factors combined with professional-personal ones to shape their decisions. The paper further uses their experiences to demonstrate the importance of transnational scientific interactions for the development of science in China, the US, and elsewhere in the twentieth century. Keywords: Shiing-shen Chern, Chen Xingshen, Hua Luogeng, Loo-Keng Hua, Institute for 1 This article was copy-edited by Charlie Zaharoff. 2 Research interests: History of science and technology in the United States, China, and transnational contexts in the twentieth century. He is currently writing a book on the history of American-educated Chinese scientists and China-US scientific relations. -
Analysis of the Riemann Problem for a Shallow Water Model with Two Velocities Nina Aguillon, Emmanuel Audusse, Edwige Godlewski, Martin Parisot
Analysis of the Riemann Problem for a shallow water model with two velocities Nina Aguillon, Emmanuel Audusse, Edwige Godlewski, Martin Parisot To cite this version: Nina Aguillon, Emmanuel Audusse, Edwige Godlewski, Martin Parisot. Analysis of the Riemann Problem for a shallow water model with two velocities. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2018, 10.1137/17M1152887. hal-01618722v2 HAL Id: hal-01618722 https://hal.inria.fr/hal-01618722v2 Submitted on 19 Oct 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Analysis of the Riemann Problem for a shallow water model with two velocities Nina Aguillon∗1,2, Emmanuel Audussey3, Edwige Godlewskiz1,2,4, and Martin Parisotx4,1,2 1Sorbonne Universit´es,UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France 2CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France 3Universit´eParis 13, Laboratoire d'Analyse, G´eom´etrieet Applications, 99 av. J.-B. Cl´ement, F-93430 Villetaneuse, France 4INRIA Paris, ANGE Project-Team, 75589 Paris Cedex 12, France October 18, 2017 Abstract Some shallow water type models describing the vertical profile of the horizontal velocity with several degrees of freedom have been recently pro- posed. -
Interview of Albert Tucker
University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange About Harlan D. Mills Science Alliance 9-1975 Interview of Albert Tucker Terry Speed Evar Nering Follow this and additional works at: https://trace.tennessee.edu/utk_harlanabout Part of the Mathematics Commons Recommended Citation Speed, Terry and Nering, Evar, "Interview of Albert Tucker" (1975). About Harlan D. Mills. https://trace.tennessee.edu/utk_harlanabout/13 This Report is brought to you for free and open access by the Science Alliance at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in About Harlan D. Mills by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. The Princeton Mathematics Community in the 1930s (PMC39)The Princeton Mathematics Community in the 1930s Transcript Number 39 (PMC39) © The Trustees of Princeton University, 1985 ALBERT TUCKER CAREER, PART 2 This is a continuation of the account of the career of Albert Tucker that was begun in the interview conducted by Terry Speed in September 1975. This recording was made in March 1977 by Evar Nering at his apartment in Scottsdale, Arizona. Tucker: I have recently received the tapes that Speed made and find that these tapes carried my history up to approximately 1938. So the plan is to continue the history. In the late '30s I was working in combinatorial topology with not a great deal of results to show. I guess I was really more interested in my teaching. I had an opportunity to teach an undergraduate course in topology, combinatorial topology that is, classification of 2-dimensional surfaces and that sort of thing. -
The History of the Abel Prize and the Honorary Abel Prize the History of the Abel Prize
The History of the Abel Prize and the Honorary Abel Prize The History of the Abel Prize Arild Stubhaug On the bicentennial of Niels Henrik Abel’s birth in 2002, the Norwegian Govern- ment decided to establish a memorial fund of NOK 200 million. The chief purpose of the fund was to lay the financial groundwork for an annual international prize of NOK 6 million to one or more mathematicians for outstanding scientific work. The prize was awarded for the first time in 2003. That is the history in brief of the Abel Prize as we know it today. Behind this government decision to commemorate and honor the country’s great mathematician, however, lies a more than hundred year old wish and a short and intense period of activity. Volumes of Abel’s collected works were published in 1839 and 1881. The first was edited by Bernt Michael Holmboe (Abel’s teacher), the second by Sophus Lie and Ludvig Sylow. Both editions were paid for with public funds and published to honor the famous scientist. The first time that there was a discussion in a broader context about honoring Niels Henrik Abel’s memory, was at the meeting of Scan- dinavian natural scientists in Norway’s capital in 1886. These meetings of natural scientists, which were held alternately in each of the Scandinavian capitals (with the exception of the very first meeting in 1839, which took place in Gothenburg, Swe- den), were the most important fora for Scandinavian natural scientists. The meeting in 1886 in Oslo (called Christiania at the time) was the 13th in the series. -
Möbel Und Einrichtungsgegenstände
16 Möbel und Einrichtungsgegenstände 1001 1002 Möbel und Einrichtungsgegenstände 1001. Ein Paar Encoignuren, Barock, Italien, 17. Jh. Nadelholz. Abgerundete, eintürige Korpusse auf Konsolenbeinen. Das Blatt aus jüngerer Zeit, mit grünem Marmor. 116:61:48 cm und 112:60:45 cm. 1500.—/1800.— Provenienz: Italienischer Privatbesitz Aus einem Schloss in der Westschweiz 1002. Prie-dieu, Norditalien, Toskana, circa 1700. Nussholz, massiv. Auf massiven Eckkonsolen, mit profi- liertem Sockel und klappbarem Fach. Zurückversetztes, zweitüriges Schrankfach, darüber eine Schublade und wenig vorstehende Deckplatte. 82:62:54 cm. 500.—/700.— Provenienz: Italienischer Privatbesitz Aus einem Schloss in der Westschweiz 1003. Zwei Dominikanermönche, burgundischer Meister, um 1450. Beide Figuren in kräftig gefaltetem Habit, die Ge- sichter individuell und charaktervoll geschnitzt. Die Köpfe bedeckt mit Kapuze, über der Stirn der schmale Haarkreis der Tonsur. Die grössere Figur hält in den Händen ein auf- geschlagenes Buch, die kleinere Figur in der Rechten ein Bruchstück eines verlustigen Abtstabes. Die linke Hand fehlt. Nussbaum, geschnitzt, mit Originalfassung. Rückseitig gehöhlt. H = 115 cm und H = 111,5 cm. 6000.—/8000.— Provenienz: Sammlung Elsa Bloch-Diener Die beiden hier zum Verkauf kommenden Skulpturen zweier Mönche, welche sich über ein halbes Jahrhundert im Besitze von Elsa Bloch-Diener befanden, stammen aus der Zeit, als das Reich der Herzöge von Valois- Burgund sich praktisch vom eigentlichen Herzogtum Burgund bis zur Nord- see erstreckte und zwischen Frankreich und dem Heiligen Römischen Reich die dritte Grossmacht in Europa war. Unter dem umsichtigen Herzog Philipp dem Guten (1396–1467) stand dieses Mittelreich in seiner wirtschaftlichen und kulturellen Blüte. Die besten Künstler aus diesem Reich, wozu auch die Niederlande gehörte, arbeiteten für den Hof. -
The Materiality & Ontology of Digital Subjectivity
THE MATERIALITY & ONTOLOGY OF DIGITAL SUBJECTIVITY: GRIGORI “GRISHA” PERELMAN AS A CASE STUDY IN DIGITAL SUBJECTIVITY A Thesis Submitted to the Committee on Graduate Studies in Partial Fulfillment of the Requirements for the Degree of Master of Arts in the Faculty of Arts and Science TRENT UNIVERSITY Peterborough, Ontario, Canada Copyright Gary Larsen 2015 Theory, Culture, and Politics M.A. Graduate Program September 2015 Abstract THE MATERIALITY & ONTOLOGY OF DIGITAL SUBJECTIVITY: GRIGORI “GRISHA” PERELMAN AS A CASE STUDY IN DIGITAL SUBJECTIVITY Gary Larsen New conditions of materiality are emerging from fundamental changes in our ontological order. Digital subjectivity represents an emergent mode of subjectivity that is the effect of a more profound ontological drift that has taken place, and this bears significant repercussions for the practice and understanding of the political. This thesis pivots around mathematician Grigori ‘Grisha’ Perelman, most famous for his refusal to accept numerous prestigious prizes resulting from his proof of the Poincaré conjecture. The thesis shows the Perelman affair to be a fascinating instance of the rise of digital subjectivity as it strives to actualize a new hegemonic order. By tracing first the production of aesthetic works that represent Grigori Perelman in legacy media, the thesis demonstrates that there is a cultural imperative to represent Perelman as an abject figure. Additionally, his peculiar abjection is seen to arise from a challenge to the order of materiality defended by those with a vested interest in maintaining the stability of a hegemony identified with the normative regulatory power of the heteronormative matrix sustaining social relations in late capitalism. -
Fundamental Theorems in Mathematics
SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635]. -
Of Triangles, Gas, Price, and Men
OF TRIANGLES, GAS, PRICE, AND MEN Cédric Villani Univ. de Lyon & Institut Henri Poincaré « Mathematics in a complex world » Milano, March 1, 2013 Riemann Hypothesis (deepest scientific mystery of our times?) Bernhard Riemann 1826-1866 Riemann Hypothesis (deepest scientific mystery of our times?) Bernhard Riemann 1826-1866 Riemannian (= non-Euclidean) geometry At each location, the units of length and angles may change Shortest path (= geodesics) are curved!! Geodesics can tend to get closer (positive curvature, fat triangles) or to get further apart (negative curvature, skinny triangles) Hyperbolic surfaces Bernhard Riemann 1826-1866 List of topics named after Bernhard Riemann From Wikipedia, the free encyclopedia Riemann singularity theorem Cauchy–Riemann equations Riemann solver Compact Riemann surface Riemann sphere Free Riemann gas Riemann–Stieltjes integral Generalized Riemann hypothesis Riemann sum Generalized Riemann integral Riemann surface Grand Riemann hypothesis Riemann theta function Riemann bilinear relations Riemann–von Mangoldt formula Riemann–Cartan geometry Riemann Xi function Riemann conditions Riemann zeta function Riemann curvature tensor Zariski–Riemann space Riemann form Riemannian bundle metric Riemann function Riemannian circle Riemann–Hilbert correspondence Riemannian cobordism Riemann–Hilbert problem Riemannian connection Riemann–Hurwitz formula Riemannian cubic polynomials Riemann hypothesis Riemannian foliation Riemann hypothesis for finite fields Riemannian geometry Riemann integral Riemannian graph Bernhard -
An Interview with Martin Davis
Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Geometry Ramanujan‘s Lost Notebook An Introduction to Mathematical of the American Mathematical Society Selected Topics in Plane and Solid Part II Cryptography May 2008 Volume 55, Number 5 Geometry G. E. Andrews, Penn State University, University J. Hoffstein, J. Pipher, J. Silverman, Brown J. Aarts, Delft University of Technology, Park, PA, USA; B. C. Berndt, University of Illinois University, Providence, RI, USA Mediamatics, The Netherlands at Urbana, IL, USA This self-contained introduction to modern This is a book on Euclidean geometry that covers The “lost notebook” contains considerable cryptography emphasizes the mathematics the standard material in a completely new way, material on mock theta functions—undoubtedly behind the theory of public key cryptosystems while also introducing a number of new topics emanating from the last year of Ramanujan’s life. and digital signature schemes. The book focuses Interview with Martin Davis that would be suitable as a junior-senior level It should be emphasized that the material on on these key topics while developing the undergraduate textbook. The author does not mock theta functions is perhaps Ramanujan’s mathematical tools needed for the construction page 560 begin in the traditional manner with abstract deepest work more than half of the material in and security analysis of diverse cryptosystems. geometric axioms. Instead, he assumes the real the book is on q- series, including mock theta Only basic linear algebra is required of the numbers, and begins his treatment by functions; the remaining part deals with theta reader; techniques from algebra, number theory, introducing such modern concepts as a metric function identities, modular equations, and probability are introduced and developed as space, vector space notation, and groups, and incomplete elliptic integrals of the first kind and required. -
Scientific Workplace· • Mathematical Word Processing • LATEX Typesetting Scientific Word· • Computer Algebra
Scientific WorkPlace· • Mathematical Word Processing • LATEX Typesetting Scientific Word· • Computer Algebra (-l +lr,:znt:,-1 + 2r) ,..,_' '"""""Ke~r~UrN- r o~ r PooiliorK 1.931'J1 Po6'lf ·1.:1l26!.1 Pod:iDnZ 3.881()2 UfW'IICI(JI)( -2.801~ ""'"""U!NecteoZ l!l!iS'11 v~ 0.7815399 Animated plots ln spherical coordln1tes > To make an anlm.ted plot In spherical coordinates 1. Type an expression In thr.. variables . 2 WMh the Insertion poilt In the expression, choose Plot 3D The next exampfe shows a sphere that grows ftom radius 1 to .. Plot 3D Animated + Spherical The Gold Standard for Mathematical Publishing Scientific WorkPlace and Scientific Word Version 5.5 make writing, sharing, and doing mathematics easier. You compose and edit your documents directly on the screen, without having to think in a programming language. A click of a button allows you to typeset your documents in LAT£X. You choose to print with or without LATEX typesetting, or publish on the web. Scientific WorkPlace and Scientific Word enable both professionals and support staff to produce stunning books and articles. Also, the integrated computer algebra system in Scientific WorkPlace enables you to solve and plot equations, animate 20 and 30 plots, rotate, move, and fly through 3D plots, create 3D implicit plots, and more. MuPAD' Pro MuPAD Pro is an integrated and open mathematical problem solving environment for symbolic and numeric computing. Visit our website for details. cK.ichan SOFTWARE , I NC. Visit our website for free trial versions of all our products. www.mackichan.com/notices • Email: info@mac kichan.com • Toll free: 877-724-9673 It@\ A I M S \W ELEGRONIC EDITORIAL BOARD http://www.math.psu.edu/era/ Managing Editors: This electronic-only journal publishes research announcements (up to about 10 Keith Burns journal pages) of significant advances in all branches of mathematics.