The problem of enumerating maps (a map is a set of polygonal ‘countries’ on aworld 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, informatics, biology,...etc . This problem has been studied by many communities of researchers, mostly combinatorists, probabilists, and physicists. In 1978+, physicists have invented a method called ‘matrix models’ to address that problem, and many results have been obtained. Beside, 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 of complicated topology. The number of Riemann surfaces is the volume of that moduli space First book on explaining the random matrix method to enumerate maps and Riemann surfaces. The method has been discovered recently (between2004 and 2007), and is presently explained only in very few specialized articles
- ISBN: 978-3-7643-8796-9
- Editorial: Birkhaüser
- Encuadernacion: Cartoné
- Páginas: 150
- Fecha Publicación: 01/02/2009
- Nº Volúmenes: 1
- Idioma: Inglés