DOCSLIB.ORG

Field Medalists

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Field Medalists Fields Medal Winners Affiliated with the Institute for Advanced Study as of August 14, 2014 f First Term s Second Term o Other 1936 Lars V. Ahlfors (Member, School of Mathematics, 1962f; 1966–67) Finland Jesse Douglas (Member, School of Mathematics, 1934–35, 1938–39) United States 1950 Atle Selberg (Professor, School of Mathematics, 1951–87; Professor Emeritus, School of Mathematics, 1987–2007; Permanent Member, School of Mathematics, 1949–51; Member, School of Mathematics, 1947–48) Norway 1954 Kunihiko Kodaira (Member, School of Mathematics, 1949–50, 1951–52, 1956s, 1957s, 1958s, 1959s, 1960s, 1961s) Japan Jean-Pierre Serre (Member, School of Mathematics, 1955–58, 1959–60, 1961–62, 1962f, 1972, 1967–68, 1970–71, 1972–73, 1978s, 1983–84; Visitor, School of Mathematics, 1963–64, 1999f) France 1958 René Thom (Member, School of Mathematics, 1956f, 1961–62) France 1962 Lars Valter Hörmander (Professor, School of Mathematics, 1964–68; Member, School of Mathematics, 1960–61, 1971s, 1977–78) Sweden John Willard Milnor (Professor, School of Mathematics, 1970–90; Member, School of Mathematics, 1966s; Visitor, School of Mathematics, 1999f, 2002o) United States 1966 Michael Atiyah (Professor, School of Mathematics, 1969–72; Member, School of Mathematics, 1955–56, 1956f, 1959f, 1976f, 1987f) United Kingdom Paul J. Cohen (Member, School of Mathematics, 1959–61, 1967f) United States Stephen Smale (Member, School of Mathematics, 1958–60, 1966–67) United States Office of Public Affairs Phone (609) 951-4458 • Fax (609) 951-4451 • www.ias.edu 1970 Alan Baker (Member, School of Mathematics, 1970f) United Kingdom Heisuke Hironaka (Member, School of Mathematics, 1962–63) Japan John G. Thompson (Member, School of Mathematics, 1978f) United States 1974 Enrico Bombieri (IBM Von Neumann Professor, School of Mathematics, 1984–2011; Professor, School of Mathematics, 1977–1984; Professor Emeritus, School of Mathematics, 2011–present; Member, School of Mathematics, 1974s) Italy David B. Mumford (Member, School of Mathematics, 1962–63, 1981–82) United States 1978 Pierre Deligne (Professor, School of Mathematics, 1984–2007; Professor Emeritus, School of Mathematics, 2008–present; Member, School of Mathematics, 1972–73, 1977s; Visitor, School of Mathematics, 1981f) Belgium Grigori Margulis (Member, School of Mathematics, 1991s, 2006s) Russia Daniel G. Quillen (Member, School of Mathematics, 1969–70) United States 1982 Alain Connes (Member, School of Mathematics, 1978–79) France William P. Thurston (Member, School of Mathematics, 1972–73, 1976s, 1984–85) United States Shing-Tung Yau (Professor, School of Mathematics, 1980–84; Member, School of Mathematics, 1971–72, 1979–80) China 1986 Simon K. Donaldson (Member, School of Mathematics, 1983–84) United Kingdom Gerd Faltings (Member, School of Mathematics, 1988f, 1992–93) Germany Michael H. Freedman (Member, School of Mathematics, 1975–76, 1980–81) United States 1990 Vladimir Drinfeld (Member, School of Mathematics, 1990s, 1997s, 1998s) Russia Shigefumi Mori (Member, School of Mathematics, 1981–82) Japan Edward Witten (Charles Simonyi Professor, School of Natural Sciences, 1997–present; Professor, School of Natural Sciences, 1987–1997; Member, School of Natural Sciences, 1984s) United States 1994 Jean Bourgain (Professor, School of Mathematics, 1994–present) Belgium 1998 Maxim Kontsevich (Joint Member, Schools of Mathematics and Natural Sciences 1992–93; Visitor, School of Mathematics, 2002s) Russia Curtis T. McMullen (Member, School of Mathematics, 1986–87) United States Andrew Wiles [Fields Silver Plate recipient] (Institute Trustee, 2007–present; Member, School of Mathematics, 1981–82, 1992s, 1995–96, 1998s, 1999s, 2000s, 2001s, 2002s, 2003s, 2004s; Visitor, School of Mathematics, 2007–11) United Kingdom 2002 Vladimir Voevodsky (Professor, School of Mathematics, 2002–present; Member, School of Mathematics, 1992–93, 1998–2001) Russia 2006 Andrei Okounkov (Member, School of Mathematics, 1996s) Russia 2010 Elon Lindenstrauss (Member, School of Mathematics, 2000–01, 2007f; Visitor, School of Mathematics, 2009–10) Israel Bao Châu Ngô (Member, School of Mathematics, 2006f, 2007–10) Vietnam Stanislav Smirnov (Member, School of Mathematics, 1998s, 2003s) Russia Cédric Villani (Member, School of Mathematics, 2009s) France 2014 Manjul Bharğava (Member, School of Mathematics, 2001–02) Canada Martin Hairer (Member, School of Mathematics, 2014s) Austria .
Load more

Recommended publications
  • A MATHEMATICIAN's SURVIVAL GUIDE 1. an Algebra Teacher I
    A MATHEMATICIAN’S SURVIVAL GUIDE PETER G. CASAZZA 1. An Algebra Teacher I could Understand Emmy award-winning journalist and bestselling author Cokie Roberts once said: As long as algebra is taught in school, there will be prayer in school. 1.1. An Object of Pride. Mathematician’s relationship with the general public most closely resembles “bipolar” disorder - at the same time they admire us and hate us. Almost everyone has had at least one bad experience with mathematics during some part of their education. Get into any taxi and tell the driver you are a mathematician and the response is predictable. First, there is silence while the driver relives his greatest nightmare - taking algebra. Next, you will hear the immortal words: “I was never any good at mathematics.” My response is: “I was never any good at being a taxi driver so I went into mathematics.” You can learn a lot from taxi drivers if you just don’t tell them you are a mathematician. Why get started on the wrong foot? The mathematician David Mumford put it: “I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate.” 1.2. A Balancing Act. The other most common response we get from the public is: “I can’t even balance my checkbook.” This reflects the fact that the public thinks that mathematics is basically just adding numbers. They have no idea what we really do. Because of the textbooks they studied, they think that all needed mathematics has already been discovered.
    [Show full text]
  • Report for the Academic Year 1995
    Institute /or ADVANCED STUDY REPORT FOR THE ACADEMIC YEAR 1994 - 95 PRINCETON NEW JERSEY Institute /or ADVANCED STUDY REPORT FOR THE ACADEMIC YEAR 1 994 - 95 OLDEN LANE PRINCETON • NEW JERSEY 08540-0631 609-734-8000 609-924-8399 (Fax) Extract from the letter addressed by the Founders to the Institute's Trustees, dated June 6, 1930. Newark, New jersey. It is fundamental in our purpose, and our express desire, that in the appointments to the staff and faculty, as well as in the admission of workers and students, no account shall be taken, directly or indirectly, of race, religion, or sex. We feel strongly that the spirit characteristic of America at its noblest, above all the pursuit of higher learning, cannot admit of any conditions as to personnel other than those designed to promote the objects for which this institution is established, and particularly with no regard whatever to accidents of race, creed, or sex. TABLE OF CONTENTS 4 BACKGROUND AND PURPOSE 5 • FOUNDERS, TRUSTEES AND OFFICERS OF THE BOARD AND OF THE CORPORATION 8 • ADMINISTRATION 11 REPORT OF THE CHAIRMAN 15 REPORT OF THE DIRECTOR 23 • ACKNOWLEDGMENTS 27 • REPORT OF THE SCHOOL OF HISTORICAL STUDIES ACADEMIC ACTIVITIES MEMBERS, VISITORS AND RESEARCH STAFF 36 • REPORT OF THE SCHOOL OF MATHEMATICS ACADEMIC ACTIVITIES MEMBERS AND VISITORS 42 • REPORT OF THE SCHOOL OF NATURAL SCIENCES ACADEMIC ACTIVITIES MEMBERS AND VISITORS 50 • REPORT OF THE SCHOOL OF SOCIAL SCIENCE ACADEMIC ACTIVITIES MEMBERS, VISITORS AND RESEARCH STAFF 55 • REPORT OF THE INSTITUTE LIBRARIES 57 • RECORD OF INSTITUTE EVENTS IN THE ACADEMIC YEAR 1994-95 85 • INDEPENDENT AUDITORS' REPORT INSTITUTE FOR ADVANCED STUDY: BACKGROUND AND PURPOSE The Institute for Advanced Study is an independent, nonprofit institution devoted to the encouragement of learning and scholarship.
    [Show full text]
  • MY UNFORGETTABLE EARLY YEARS at the INSTITUTE Enstitüde Unutulmaz Erken Yıllarım
    MY UNFORGETTABLE EARLY YEARS AT THE INSTITUTE Enstitüde Unutulmaz Erken Yıllarım Dinakar Ramakrishnan `And what was it like,’ I asked him, `meeting Eliot?’ `When he looked at you,’ he said, `it was like standing on a quay, watching the prow of the Queen Mary come towards you, very slowly.’ – from `Stern’ by Seamus Heaney in memory of Ted Hughes, about the time he met T.S.Eliot It was a fortunate stroke of serendipity for me to have been at the Institute for Advanced Study in Princeton, twice during the nineteen eighties, first as a Post-doctoral member in 1982-83, and later as a Sloan Fellow in the Fall of 1986. I had the privilege of getting to know Robert Langlands at that time, and, needless to say, he has had a larger than life influence on me. It wasn’t like two ships passing in the night, but more like a rowboat feeling the waves of an oncoming ship. Langlands and I did not have many conversations, but each time we did, he would make a Zen like remark which took me a long time, at times months (or even years), to comprehend. Once or twice it even looked like he was commenting not on the question I posed, but on a tangential one; however, after much reflection, it became apparent that what he had said had an interesting bearing on what I had been wondering about, and it always provided a new take, at least to me, on the matter. Most importantly, to a beginner in the field like I was then, he was generous to a fault, always willing, whenever asked, to explain the subtle aspects of his own work.
    [Show full text]
  • Homogeneous Flows, Moduli Spaces and Arithmetic
    CLAY MATHEMATICS INSTITUTE SUMMER SCHOOL 2007 Homogeneous Flows, Moduli Spaces and Arithmetic at the Centro di Ricerca Matematica Designed for graduate students and mathematicians within Ennio De Giorgi, Pisa, Italy five years of their PhD, the program is an introduction to the theory of flows on homogeneous spaces, moduli spaces and their many applications. These flows give concrete examples of dynamical systems with highly interesting behavior and a rich and powerful theory. They are also a source of many interesting problems and conjectures. Furthermore, understanding the dynamics of such a concrete system lends to numerous applications in number theory and geometry regarding equidistributions, diophantine approximations, rational billiards and automorphic forms. The school will consist of three weeks of foundational courses Photo: Peter Adams and one week of mini-courses focusing on more advanced topics. June 11th to July 6th 2007 Lecturers to include: Organizing Committee Nalini Anantharaman, Artur Avila, Manfred Einsiedler, Alex Eskin, Manfred Einsiedler, David Ellwood, Alex Eskin, Dmitry Kleinbock, Elon Svetlana Katok, Dmitry Kleinbock, Elon Lindenstrauss, Shahar Mozes, Lindenstrauss, Gregory Margulis, Stefano Marmi, Peter Sarnak, Hee Oh, Akshay Venkatesh, Jean-Christophe Yoccoz Jean-Christophe Yoccoz, Don Zagier Foundational Courses Graduate Postdoctoral Funding Unipotent flows and applications Funding is available to graduate students and postdoctoral fellows (within 5 Alex Eskin & Dmitry Kleinbock years of their PhD). Standard
    [Show full text]
  • Diagonalizable Flows on Locally Homogeneous Spaces and Number
    Diagonalizable flows on locally homogeneous spaces and number theory Manfred Einsiedler and Elon Lindenstrauss∗ Abstract.We discuss dynamical properties of actions of diagonalizable groups on locally homogeneous spaces, particularly their invariant measures, and present some number theoretic and spectral applications. Entropy plays a key role in the study of theses invariant measures and in the applications. Mathematics Subject Classification (2000). 37D40, 37A45, 11J13, 81Q50 Keywords. invariant measures, locally homogeneous spaces, Littlewood’s conjecture, quantum unique ergodicity, distribution of periodic orbits, ideal classes, entropy. 1. Introduction Flows on locally homogeneous spaces are a special kind of dynamical systems. The ergodic theory and dynamics of these flows are very rich and interesting, and their study has a long and distinguished history. What is more, this study has found numerous applications throughout mathematics. The spaces we consider are of the form Γ\G where G is a locally compact group and Γ a discrete subgroup of G. Typically one takes G to be either a Lie group, a linear algebraic group over a local field, or a product of such. Any subgroup H < G acts on Γ\G and this action is precisely the type of action we will consider here. One of the most important examples which features in numerous number theoretical applications is the space PGL(n, Z)\ PGL(n, R) which can be identified with the space of lattices in Rn up to homothety. Part of the beauty of the subject is that the study of very concrete actions can have meaningful implications. For example, in the late 1980s G.
    [Show full text]
  • 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,
    [Show full text]
  • Institut Des Hautes Ét Udes Scientifiques
    InstItut des Hautes É t u d e s scIentIfIques A foundation in the public interest since 1981 2 | IHES IHES | 3 Contents A VISIONARY PROJECT, FOR EXCELLENCE IN SCIENCE P. 5 Editorial P. 6 Founder P. 7 Permanent professors A MODERN-DAY THELEMA FOR A GLOBAL SCIENTIFIC COMMUNITY P. 8 Research P. 9 Visitors P. 10 Events P. 11 International INDEPENDENCE AND FREEDOM, ­­ THE INSTITUTE’S TWO OPERATIONAL PILLARS P. 12 Finance P. 13 Governance P. 14 Members P. 15 Tax benefits The Marilyn and James Simons Conference Center The aim of the Foundation known as ‘Institut des Hautes Études Scientifiques’ is to enable and encourage theoretical scientific research (…). [Its] activity consists mainly in providing the Institute’s professors and researchers, both permanent and invited, with the resources required to undertake disinterested IHES February 2016 Content: IHES Communication Department – Translation: Hélène Wilkinson – Design: blossom-creation.com research. Photo Credits: Valérie Touchant-Landais / IHES, Marie-Claude Vergne / IHES – Cover: unigma All rights reserved Extract from the statutes of the Institut des Hautes Études Scientifiques, 1958. 4 | IHES IHES | 5 A visionary project, for excellence in science Editorial Emmanuel Ullmo, Mathematician, IHES Director A single scientific program: curiosity. A single selection criterion: excellence. The Institut des Hautes Études Scientifiques is an international mathematics and theoretical physics research center. Free of teaching duties and administrative tasks, its professors and visitors undertake research in complete independence and total freedom, at the highest international level. Ever since it was created, IHES has cultivated interdisciplinarity. The constant dialogue between mathematicians and theoretical physicists has led to particularly rich interactions.
    [Show full text]
  • Why U.S. Immigration Barriers Matter for the Global Advancement of Science
    DISCUSSION PAPER SERIES IZA DP No. 14016 Why U.S. Immigration Barriers Matter for the Global Advancement of Science Ruchir Agarwal Ina Ganguli Patrick Gaulé Geoff Smith JANUARY 2021 DISCUSSION PAPER SERIES IZA DP No. 14016 Why U.S. Immigration Barriers Matter for the Global Advancement of Science Ruchir Agarwal Patrick Gaulé International Monetary Fund University of Bath and IZA Ina Ganguli Geoff Smith University of Massachusetts Amherst University of Bath JANUARY 2021 Any opinions expressed in this paper are those of the author(s) and not those of IZA. Research published in this series may include views on policy, but IZA takes no institutional policy positions. The IZA research network is committed to the IZA Guiding Principles of Research Integrity. The IZA Institute of Labor Economics is an independent economic research institute that conducts research in labor economics and offers evidence-based policy advice on labor market issues. Supported by the Deutsche Post Foundation, IZA runs the world’s largest network of economists, whose research aims to provide answers to the global labor market challenges of our time. Our key objective is to build bridges between academic research, policymakers and society. IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be available directly from the author. ISSN: 2365-9793 IZA – Institute of Labor Economics Schaumburg-Lippe-Straße 5–9 Phone: +49-228-3894-0 53113 Bonn, Germany Email: [email protected] www.iza.org IZA DP No. 14016 JANUARY 2021 ABSTRACT Why U.S.
    [Show full text]
  • Sir Andrew J. Wiles
    ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society March 2017 Volume 64, Number 3 Women's History Month Ad Honorem Sir Andrew J. Wiles page 197 2018 Leroy P. Steele Prize: Call for Nominations page 195 Interview with New AMS President Kenneth A. Ribet page 229 New York Meeting page 291 Sir Andrew J. Wiles, 2016 Abel Laureate. “The definition of a good mathematical problem is the mathematics it generates rather Notices than the problem itself.” of the American Mathematical Society March 2017 FEATURES 197 239229 26239 Ad Honorem Sir Andrew J. Interview with New The Graduate Student Wiles AMS President Kenneth Section Interview with Abel Laureate Sir A. Ribet Interview with Ryan Haskett Andrew J. Wiles by Martin Raussen and by Alexander Diaz-Lopez Allyn Jackson Christian Skau WHAT IS...an Elliptic Curve? Andrew Wiles's Marvelous Proof by by Harris B. Daniels and Álvaro Henri Darmon Lozano-Robledo The Mathematical Works of Andrew Wiles by Christopher Skinner In this issue we honor Sir Andrew J. Wiles, prover of Fermat's Last Theorem, recipient of the 2016 Abel Prize, and star of the NOVA video The Proof. We've got the official interview, reprinted from the newsletter of our friends in the European Mathematical Society; "Andrew Wiles's Marvelous Proof" by Henri Darmon; and a collection of articles on "The Mathematical Works of Andrew Wiles" assembled by guest editor Christopher Skinner. We welcome the new AMS president, Ken Ribet (another star of The Proof). Marcelo Viana, Director of IMPA in Rio, describes "Math in Brazil" on the eve of the upcoming IMO and ICM.
    [Show full text]
  • A Short Survey of Cyclic Cohomology
    Clay Mathematics Proceedings Volume 10, 2008 A Short Survey of Cyclic Cohomology Masoud Khalkhali Dedicated with admiration and affection to Alain Connes Abstract. This is a short survey of some aspects of Alain Connes’ contribu- tions to cyclic cohomology theory in the course of his work on noncommutative geometry over the past 30 years. Contents 1. Introduction 1 2. Cyclic cohomology 3 3. From K-homology to cyclic cohomology 10 4. Cyclic modules 13 5. Thelocalindexformulaandbeyond 16 6. Hopf cyclic cohomology 21 References 28 1. Introduction Cyclic cohomology was discovered by Alain Connes no later than 1981 and in fact it was announced in that year in a conference in Oberwolfach [5]. I have reproduced the text of his abstract below. As it appears in his report, one of arXiv:1008.1212v1 [math.OA] 6 Aug 2010 Connes’ main motivations to introduce cyclic cohomology theory came from index theory on foliated spaces. Let (V, ) be a compact foliated manifold and let V/ denote the space of leaves of (V, ).F This space, with its natural quotient topology,F is, in general, a highly singular spaceF and in noncommutative geometry one usually replaces the quotient space V/ with a noncommutative algebra A = C∗(V, ) called the foliation algebra of (V,F ). It is the convolution algebra of the holonomyF groupoid of the foliation and isF a C∗-algebra. It has a dense subalgebra = C∞(V, ) which plays the role of the algebra of smooth functions on V/ . LetA D be a transversallyF elliptic operator on (V, ). The analytic index of D, index(F D) F ∈ K0(A), is an element of the K-theory of A.
    [Show full text]
  • Occasion of Receiving the Seki-Takakazu Prize
    特集：日本数学会関孝和賞受賞 On the occasion of receiving the Seki-Takakazu Prize Jean-Pierre Bourguignon, the director of IHÉS A brief introduction to the Institut des Hautes Études Scientifiques The Institut des Hautes Études Scientifiques (IHÉS) was founded in 1958 by Léon MOTCHANE, an industrialist with a passion for mathematics, whose ambition was to create a research centre in Europe, counterpart to the renowned Institute for Advanced Study (IAS), Princeton, United States. IHÉS became a foundation acknowledged in the public interest in 1981. Like its model, IHÉS has a small number of Permanent Professors (5 presently), and hosts every year some 250 visitors coming from all around the world. A Scientific Council consisting of the Director, the Permanent Professors, the Léon Motchane professor and an equal number of external members is in charge of defining the scientific strategy of the Institute. The foundation is managed by an 18 member international Board of Directors selected for their expertise in science or in management. The French Minister of Research or their representative and the General Director of CNRS are members of the Board. IHÉS accounts are audited and certified by an international accountancy firm, Deloitte, Touche & Tomatsu. Its resources come from many different sources: half of its budget is provided by a contract with the French government, but institutions from some 10 countries, companies, foundations provide the other half, together with the income from the endowment of the Institute. Some 50 years after its creation, the high quality of its Permanent Professors and of its selected visiting researchers has established IHÉS as a research institute of world stature.
    [Show full text]
  • Density of Algebraic Points on Noetherian Varieties 3
    DENSITY OF ALGEBRAIC POINTS ON NOETHERIAN VARIETIES GAL BINYAMINI Abstract. Let Ω ⊂ Rn be a relatively compact domain. A finite collection of real-valued functions on Ω is called a Noetherian chain if the partial derivatives of each function are expressible as polynomials in the functions. A Noether- ian function is a polynomial combination of elements of a Noetherian chain. We introduce Noetherian parameters (degrees, size of the coefficients) which measure the complexity of a Noetherian chain. Our main result is an explicit form of the Pila-Wilkie theorem for sets defined using Noetherian equalities and inequalities: for any ε> 0, the number of points of height H in the tran- scendental part of the set is at most C ·Hε where C can be explicitly estimated from the Noetherian parameters and ε. We show that many functions of interest in arithmetic geometry fall within the Noetherian class, including elliptic and abelian functions, modular func- tions and universal covers of compact Riemann surfaces, Jacobi theta func- tions, periods of algebraic integrals, and the uniformizing map of the Siegel modular variety Ag . We thus effectivize the (geometric side of) Pila-Zannier strategy for unlikely intersections in those instances that involve only compact domains. 1. Introduction 1.1. The (real) Noetherian class. Let ΩR ⊂ Rn be a bounded domain, and n denote by x := (x1,...,xn) a system of coordinates on R . A collection of analytic ℓ functions φ := (φ1,...,φℓ): Ω¯ R → R is called a (complex) real Noetherian chain if it satisfies an overdetermined system of algebraic partial differential equations, i =1,...,ℓ ∂φi = Pi,j (x, φ), (1) ∂xj j =1,...,n where P are polynomials.
    [Show full text]