Coverart for item
The Resource Counting Surfaces : CRM Aisenstadt Chair lectures, by Bertrand Eynard, (electronic resource)

Counting Surfaces : CRM Aisenstadt Chair lectures, by Bertrand Eynard, (electronic resource)

Label
Counting Surfaces : CRM Aisenstadt Chair lectures
Title
Counting Surfaces
Title remainder
CRM Aisenstadt Chair lectures
Statement of responsibility
by Bertrand Eynard
Creator
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Eynard, Bertrand
Image bit depth
0
Literary form
non fiction
Series statement
Progress in Mathematical Physics,
Series volume
70
http://library.link/vocab/subjectName
  • Mathematics
  • Algebraic geometry
  • Combinatorics
Label
Counting Surfaces : CRM Aisenstadt Chair lectures, by Bertrand Eynard, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-7643-8797-6
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
I Maps and discrete surfaces -- II Formal matrix integrals -- III Solution of Tutte-loop equations -- IV Multicut case -- V Counting large maps -- VI Counting Riemann surfaces -- VII Topological recursion and symplectic invariants -- VIII Ising model -- Index -- Bibliography
Control code
978-3-7643-8797-6
Dimensions
unknown
Edition
1st ed. 2016.
Extent
1 online resource (xvii, 414 pages)
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783764387976
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-7643-8797-6
Other physical details
109 illustrations, 47 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)945445120
Label
Counting Surfaces : CRM Aisenstadt Chair lectures, by Bertrand Eynard, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-7643-8797-6
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
I Maps and discrete surfaces -- II Formal matrix integrals -- III Solution of Tutte-loop equations -- IV Multicut case -- V Counting large maps -- VI Counting Riemann surfaces -- VII Topological recursion and symplectic invariants -- VIII Ising model -- Index -- Bibliography
Control code
978-3-7643-8797-6
Dimensions
unknown
Edition
1st ed. 2016.
Extent
1 online resource (xvii, 414 pages)
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783764387976
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-7643-8797-6
Other physical details
109 illustrations, 47 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)945445120

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