Author: Leila Schneps
Published Date: 01 Dec 1994
Publisher: CAMBRIDGE UNIVERSITY PRESS
Language: English
Book Format: Paperback::380 pages
ISBN10: 0521478219
ISBN13: 9780521478212
File size: 10 Mb
Dimension: 152x 229x 21mm::560g
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Cambridge Core - Algebra - The Grothendieck Theory of Dessins d'Enfants - Leila Schneps Skip to main content We use cookies to distinguish you from other users and to provide you with a better experience on our websites. In mathematics, a dessin d'enfant is a type of graph embedding used to study Riemann (1994), The Grothendieck Theory of Dessins d'Enfants, London Grothendieck s dessins d enfants are applied to the theory of the sixth Painlevé and Gauss hypergeometric functions, two classical special functions of isomonodromy type. It is shown that higher-order transformations and the Schwarz table for the Gauss hypergeometric function are closely related to some particular Belyĭ functions. a Dessin d Enfant? Leonardo Zapponi 788 NOTICES OF THE AMS VOLUME 50, NUMBER 7 question in the theory of dessins is this: Can the The Grothendieck Theory of Dessins d Enfants, London Math. Soc. Lecture Note Ser., vol. 200, Cambridge Univ. Press, 1994. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Grothendieck's theory of Dessins d'Enfants involves combinatorially determined affine, reflective, and conformal structures on compact surfaces. In this paper the authors establish the first general method for uniformizing these dessin surfaces and for approximating their associated Belyi meromorphic The Grothendieck Theory of Dessins d'Enfant. London Math. Soc. Lecture Notes 200, Cambridge Univ. Press, 1994. Dessins d'enfants on the Riemann sphere. In the rest of the paper we give a conceptual explanation for the technique which we use in our calculations. It turns out that the classical action of the Grothendieck-Teichmüller group on dessins d enfants can be refined to an action on G-dessins,which we define, and this elucidates much of the first part. Buy The Grothendieck Theory of Dessins d'Enfants (London Mathematical Society Lecture Note Series) on FREE SHIPPING on qualified orders The theory of dessins d'enfants ("children's drawings") was part of plan started A. Grothendieck in the mid-1980's to study the interplay between Galois theory over Q and Riemann surfaces via simple and concrete combinatorial objects. We develop a p-adic version of the so-called Grothendieck-Teichmüller theory (which studies Gal (Q / Q) means of its action on profinite braid groups or mapping class groups). For every place v of Q,we give some geometrico-combinatorial descriptions of the local Galois group Gal ( Q v / Q v ) inside Gal ( Q / Q ). Grothendieck's dessins d'enfants arise with ever-increasing frequency in many areas of 21st century mathematical physics. In this paper, we review the connections between dessins and the theory of Hecke groups. Focussing on the restricted class of highly symmetric dessins corresponding to the so-called Archimedean solids, we apply this theory in order to provide a Abstract For each finite group G, we define the Grothendieck-Teichm"uller group of G, denoted GT(G), and explore its properties. The theory of dessins d'enfants shows that the inverse limit of GT(G) as G varies can be identified with a group defined Drinfeld and containing the absolute Galois group of the rational field. In Leila Schneps - Dessins d'enfants on the Riemann Sphere you can find a They appeared before L. Schneps book The Grothendieck theory of dessins In his 'Sketch of a Program,' Alexander Grothendieck describes a particular combinatorial structure, which he calls a dessin d'enfant (French for a child's drawing), embedded on a compact Riemann surface. These are finite, bipartite graphs with corresponding Belyi functions acting on the surface as a ramified cover of the Riemann sphere. Mathematics > Group Theory. Title:An elementary approach to dessins d'enfants and the Grothendieck-Teichmüller group. Authors:Pierre Dessins d enfants is French for children s drawings, which reflects the simple nature of these objects. A dessin d enfants is just a graph placed on a curve. Because of Belyi s theorem, Grothendieck was able to make a connection between graphs on a curve and covers of that same curve. Hence this gives a connection between dessins d The Grothendieck theory of dessins d'enfants: Fields of definition of some three point ramified field extensions @inproceedingsMalle1994TheGT, title=The Grothendieck theory of dessins d'enfants: Fields of definition of some three point ramified field extensions, author=Gunter Malle, year=1994 LMS Midlands Regional Meeting and Workshop on 'Galois covers, Grothendieck- Teichmüller theory and Dessins d enfants The 2018 LMS Midlands Regional Meeting and Workshop on ' Galois covers, Grothendieck- Teichmüller theory and Dessins d enfants was held at the University of Leicester from Monday June 4 to Thursday June 7, 2018. One of the major themes in the theory of dessins d enfants is the problem of determining wether two dessins are conjugate under the action of Gal(QjQ) or not. As Grothendieck writes, to each dessin subtle arithmetic invari-ants" are associated, which in their nature are of a combinatorial and topo-logical Klein s dessins d enfant and the buckyball. Showing among other things that the theory of dessins d enfant predates Grothendieck 100 years. He manages to do so associating to all these covers their dessins d enfants (which he calls Linienzuges), that is the pre-image of the interval [0,1] in which he marks the Abstract: We give an account of the theory of dessins d'enfants which is both elementary and self-contained. We describe the equivalence of many categories (graphs embedded nicely on surfaces, finite sets with certain permutations, certain field extensions, and some classes of algebraic curves), some of which are naturally endowed with an action of the absolute Galois Leila Schneps (born December 22, 1961) is an American mathematician, living in France, employed Centre national de la recherche scientifique, and based at the Institut de Mathématiques de Jussieu of Pierre and Marie Curie University, France, where she specializes in number theory. In addition to academic publication, she has edited several text books on
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