Read e-book online Counting Surfaces: CRM Aisenstadt Chair lectures (Progress PDF

By Bertrand Eynard

ISBN-10: 3764387963

ISBN-13: 9783764387969

The challenge of enumerating maps (a map is a collection of polygonal "countries" on an international of a undeniable topology, now not inevitably the aircraft or the sector) is a vital challenge in arithmetic and physics, and it has many functions starting from statistical physics, geometry, particle physics, telecommunications, biology, ... and so forth. This challenge has been studied by way of many groups of researchers, ordinarily combinatorists, probabilists, and physicists. due to the fact that 1978, physicists have invented a mode known as "matrix versions" to handle that challenge, and plenty of effects were obtained.

Besides, one other vital challenge in arithmetic and physics (in specific string theory), is to count number Riemann surfaces. Riemann surfaces of a given topology are parametrized via a finite variety of genuine parameters (called moduli), and the moduli area is a finite dimensional compact manifold or orbifold of complex topology. The variety of Riemann surfaces is the quantity of that moduli area. extra mostly, a huge challenge in algebraic geometry is to symbolize the moduli areas, through computing not just their volumes, but additionally different attribute numbers referred to as intersection numbers.

Witten's conjecture (which was once first proved via Kontsevich), was once the statement that Riemann surfaces should be acquired as limits of polygonal surfaces (maps), made up of a truly huge variety of very small polygons. In different phrases, the variety of maps in a definite restrict, may still supply the intersection numbers of moduli spaces.

In this ebook, we convey how that restrict occurs. The aim of this publication is to give an explanation for the "matrix version" approach, to teach the most effects bought with it, and to check it with equipment utilized in combinatorics (bijective proofs, Tutte's equations), or algebraic geometry (Mirzakhani's recursions).

The ebook intends to be self-contained and obtainable to graduate scholars, and gives accomplished proofs, numerous examples, and offers the overall formulation for the enumeration of maps on surfaces of any topology. in spite of everything, the hyperlink with extra basic subject matters equivalent to algebraic geometry, string conception, is mentioned, and specifically an evidence of the Witten-Kontsevich conjecture is provided.

<

Show description

Read Online or Download Counting Surfaces: CRM Aisenstadt Chair lectures (Progress in Mathematical Physics) PDF

Best combinatorics books

Download e-book for kindle: Pearls of Discrete Mathematics (Discrete Mathematics and Its by Martin Erickson

Tools Used to unravel Discrete Math ProblemsInteresting examples spotlight the interdisciplinary nature of this areaPearls of Discrete arithmetic offers equipment for fixing counting difficulties and different kinds of difficulties that contain discrete constructions. via fascinating examples, difficulties, theorems, and proofs, the booklet illustrates the connection of those buildings to algebra, geometry, quantity idea, and combinatorics.

New PDF release: Challenging Mathematical Problems with Elementary Solutions,

Designed for complex highschool scholars, undergraduates, graduate scholars, arithmetic academics, and any lover of mathematical demanding situations, this two-volume set deals a wide spectrum of difficult difficulties — starting from particularly easy to tremendous tricky. certainly, a few rank probably the greatest achievements of exceptional mathematicians.

Models, Algorithms, and Technologies for Network Analysis: by Boris Goldengorin,Valery A. Kalyagin,Panos M. Pardalos PDF

This quantity includes forms of papers—a number of contributions from the “Second overseas convention in community research” held in Nizhny Novgorod on might 7–9, 2012, and papers submitted to an "open demand papers" reflecting the actions of LATNA on the larger tuition for Economics. This quantity comprises many new ends up in modeling and robust algorithmic suggestions utilized to difficulties in• vehicle routing • single laptop scheduling • modern monetary markets• cell formation in team technology• brain actions of left- and right-handers• speeding up algorithms for the utmost clique problem• analysis and functions of alternative measures in clusteringThe huge variety of functions that may be defined and analyzed by way of a community brings jointly researchers, practitioners, and different clinical groups from a number of fields resembling Operations study, machine technological know-how, Transportation, power, Social Sciences, and extra.

Surveys in Set Theory (London Mathematical Society Lecture by A. R. D. Mathias PDF

This publication contains 5 expository articles and learn papers on subject matters of present curiosity in set thought and the rules of arithmetic. Articles by means of Baumgartner and Devlin introduce the reader to right forcing. this can be a improvement through Saharon Shelah of Cohen's technique which has ended in strategies of difficulties that resisted assault by way of forcing tools as initially constructed within the Nineteen Sixties.

Extra info for Counting Surfaces: CRM Aisenstadt Chair lectures (Progress in Mathematical Physics)

Sample text

Download PDF sample

Counting Surfaces: CRM Aisenstadt Chair lectures (Progress in Mathematical Physics) by Bertrand Eynard


by Anthony
4.0

Rated 4.33 of 5 – based on 38 votes

admin