The Resource Counting Surfaces : CRM Aisenstadt Chair lectures, by Bertrand Eynard, (electronic resource)
Counting Surfaces : CRM Aisenstadt Chair lectures, by Bertrand Eynard, (electronic resource)
Resource Information
The item Counting Surfaces : CRM Aisenstadt Chair lectures, by Bertrand Eynard, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Counting Surfaces : CRM Aisenstadt Chair lectures, by Bertrand Eynard, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 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 selfcontained 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 WittenKontsevich conjecture is provided
 Language
 eng
 Edition
 1st ed. 2016.
 Extent
 1 online resource (xvii, 414 pages)
 Contents

 I Maps and discrete surfaces
 II Formal matrix integrals
 III Solution of Tutteloop equations
 IV Multicut case
 V Counting large maps
 VI Counting Riemann surfaces
 VII Topological recursion and symplectic invariants
 VIII Ising model
 Index
 Bibliography
 Isbn
 9783764387976
 Label
 Counting Surfaces : CRM Aisenstadt Chair lectures
 Title
 Counting Surfaces
 Title remainder
 CRM Aisenstadt Chair lectures
 Statement of responsibility
 by Bertrand Eynard
 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 selfcontained 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 WittenKontsevich conjecture is provided
 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)
 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 Tutteloop 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
 9783764387976
 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, noncommercial 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
 10.1007/9783764387976
 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)
 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 Tutteloop 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
 9783764387976
 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, noncommercial 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
 10.1007/9783764387976
 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/CountingSurfacesCRMAisenstadtChair/h7ONE81dpI/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/CountingSurfacesCRMAisenstadtChair/h7ONE81dpI/">Counting Surfaces : CRM Aisenstadt Chair lectures, by Bertrand Eynard, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>