Format:
Online-Ressource (Approx. 70 p, digital)
ISBN:
9788876424571
Series Statement:
Publications of the Scuola Normale Superiore 4
Content:
Yves André: Galois theory beyond algebraic numbers and algebraic functions -- Nicholas M. Katz: Simple things we don’t know -- Endre Szemerédi: Is laziness paying off? -- Dan Abramovich: Moduli of algebraic and tropical curves -- Elias M. Stein: Three projection operators in complex analysis -- Shou-Wu Zhang: Congruent numbers and Heegner points.
Content:
Since 2001 the Scuola Normale Superiore di Pisa has organized the "Colloquio De Giorgi", a series of colloquium talks named after Ennio De Giorgi. The Colloquio is addressed to a general mathematical audience, and especially meant to attract graduate students and advanced undergraduate students. The lectures are intended to be not too technical, in fields of wide interest. They must provide an overview of the general topic, possibly in a historical perspective, together with a description of more recent progress. The idea of collecting the materials from these lectures and publishing them in annual volumes came out recently, as a recognition of their intrinsic mathematical interest, and also with the aim of preserving memory of these events.
Note:
Auf Homepage von Springer unter der Reihe „Publications of the Scuola Normale Superiore“ aufgeführt
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Description based upon print version of record
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Title Page; Copyright Page; Table of Contents; Preface; Colloquia held in 2001; Colloquia held in 2002; Colloquia held in 2003; Colloquia held in 2004; Colloquia held in 2005; Colloquia held in 2006; Colloquia held in 2007; Colloquia held in 2008; Colloquia held in 2009; Colloquia held in 2010; Colloquia held in 2011; Colloquia held in 2012; Contents of previous volumes:; Galois theory beyond algebraic numbers and algebraic functions; 1. Trancendental functions and Galois groups; 2. Trancendental numbers and Galois groups; Simple things we don't know; 1. An interactive game: dimension zero
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2. An interactive game: curves3. A "baby" version of the Sato-Tate conjecture; Conjecture 3.1.; 4. Integrality consequences; 5. Some test cases; References; Is laziness paying off? ("Absorbing" method); 1. Introduction; 2. Graphs; El-Zahar's Conjecture (1984); Pósa-Seymour Conjecture; Packing trees into a graph G; 3. Hypergraphs; 4. Absorbing Lemmas; References; Moduli of algebraic and tropical curves; 1. The moduli bug; 2. From elliptic curves to higher genus; 3. The problem of compactness; 4. The weighted graph of a curve; 5. The combinatorial structure of moduli space; 6. Tropical curves
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7. Moduli of tropical curves8. The question of comparison; 9. Nonarchimedean analytic geometry; 10. Making the connection; 11. Comments on the proof; References; Three projection operators in complex analysis; 1. Introduction; 2. The case n=1; 3. Cauchy integral in Cn , n〉1; some generalities; 4. Statement of the first result: the Cauchy-Leray integral; 5. Some ideas related to the proof; 6. The Szeg¨o and Bergman projections; 7. Outline of the proofs; References; Congruent numbers and Heegner points; 1. Problem; Triangular version; 2. Fermat 1659; 3. Conjectures; 4. Theorems
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5. Elliptic curvesTian's theorem; 6. Heegner method; Modular parametrization; Heegner point; COLLOQUIA; Published volumes
Additional Edition:
ISBN 9788876424557
Additional Edition:
Druckausg. Colloquium De Giorgi 2010-2012 Pisa : Edizioni della Normale, 2013 ISBN 9788876424557
Language:
English
Subjects:
Mathematics
DOI:
10.1007/978-88-7642-457-1
URL:
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URL:
Volltext
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