<電子ブック>
Counting Surfaces : CRM Aisenstadt Chair lectures / by Bertrand Eynard
(Progress in Mathematical Physics. ISSN:21971846 ; 70)
版 | 1st ed. 2016. |
---|---|
出版者 | Basel : Springer Basel : Imprint: Birkhäuser |
出版年 | 2016 |
本文言語 | 英語 |
大きさ | XVII, 414 p. 109 illus., 47 illus. in color : online resource |
著者標目 | *Eynard, Bertrand author SpringerLink (Online service) |
件 名 | LCSH:Algebraic geometry LCSH:Discrete mathematics FREE:Algebraic Geometry FREE:Discrete Mathematics |
一般注記 | The problem of enumerating maps (a map is a set of polygonal "countries" on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, ... etc. This problem has been studied by many communities of researchers, mostly combinatorists, probabilists, and physicists. Since 1978, physicists have invented a method called "matrix models" to address that problem, and many results have been obtained. Besides, another important problem in mathematics and physics (in particular string theory), is to count Riemann surfaces. Riemann surfaces of a given topology are parametrized by a finite number of real parameters (called moduli), and the moduli space is a finite dimensional compact manifold or orbifold of complicated topology. The number of Riemann surfaces is the volume of that moduli space. More generally, an important problem in algebraic geometry is to characterize the moduli spaces, by computing not only their volumes, but also other characteristic numbers called intersection numbers. Witten's conjecture (which was first proved by Kontsevich), was the assertion that Riemann surfaces can be obtained as limits of polygonal surfaces (maps), made of a very large number of very small polygons. In other words, the number of maps in a certain limit, should give the intersection numbers of moduli spaces. In this book, we show how that limit takes place. The goal of this book is to explain the "matrix model" method, to show the main results obtained with it, and to compare it with methods used in combinatorics (bijective proofs, Tutte's equations), or algebraic geometry (Mirzakhani's recursions). The book intends to be self-contained and accessible to graduate students, and provides comprehensive proofs, several examples, and gives the general formula for the enumeration of maps on surfaces of any topology. In the end, the link with more general topics such as algebraic geometry, string theory, is discussed, and in particular a proof of the Witten-Kontsevich conjecture is provided HTTP:URL=https://doi.org/10.1007/978-3-7643-8797-6 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
|
Springer eBooks | 9783764387976 |
|
電子リソース |
|
EB00233280 |
類似資料
この資料の利用統計
このページへのアクセス回数:4回
※2017年9月4日以降