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Chern-Simons Theory, Matrix Models, and Topological Strings

Marcos Mariño

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now various models where the string ... More


APPLICATIONS OF THE TOPOLOGICAL STRING/GAUGE THEORY CORRESPONDENCE

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter considers two applications of the topological string/gauge theory correspondence. The first application is to Chern-Simons knot and link invariants, and the second application is to ... More


CHERN–SIMONS THEORY AND KNOT INVARIANTS

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents various aspects of Chern-Simons theory. In a groundbreaking paper, Witten (1989) showed that Chern-Simons gauge theory, which is a quantum field theory in three dimensions, ... More


REPRINT STATISTICAL MECHANICS WITH TOPOLOGICAL CONSTRAINTS: II

S. F. Edwards

in Stealing the Gold: A celebration of the pioneering physics of Sam Edwards

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528531
eISBN:
9780191713415
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528531.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents a paper showing that the full specification of an assembly of long flexible molecules, needed for a statistical-mechanical study, requires an infinite set of topological ... More


NOTES ON ‘STATISTICAL MECHANICS WITH TOPOLOGICAL CONSTRAINTS: I & II’

Edward Witten

in Stealing the Gold: A celebration of the pioneering physics of Sam Edwards

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528531
eISBN:
9780191713415
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528531.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses Edwards' early work trying to devise a convenient description of topological constraint in order to study the statistical physics of cross-linked polymers, which is related to ... More


A SCIENTIST FOR ALL SEASONS

Sir Geoffrey Allen and F.R.S. F.R. Eng.

in Stealing the Gold: A celebration of the pioneering physics of Sam Edwards

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528531
eISBN:
9780191713415
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528531.003.0029
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter describes the history of Sam Edwards within polymer physics from the early days of his exposure, through his insights in seeing what is important, bringing key new insights, inspiring ... More


The Gordian Knot

David A. Shore and Eric D. Kupferberg

in High Stakes: The Critical Role of Stakeholders in Health Care

Published in print:
2011
Published Online:
September 2011
ISBN:
9780195326253
eISBN:
9780199897285
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195326253.003.0012
Subject:
Public Health and Epidemiology, Public Health

This chapter looks at the value in health care in the United States. Section 2.1 considers what we get for the dollars spent in the United States. Section 2.2 identifies the price inflators that are ... More


Lectures on Geometry

Edward Witten, Martin Bridson, Helmut Hofer, Marc Lackenby, and Rahul Pandharipande

N M J Woodhouse (ed.)

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198784913
eISBN:
9780191827150
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198784913.001.0001
Subject:
Mathematics, Geometry / Topology

This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years. Although not explicitly linked, ... More


4-Manifolds

Selman Akbulut

Published in print:
2016
Published Online:
November 2016
ISBN:
9780198784869
eISBN:
9780191827136
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198784869.001.0001
Subject:
Mathematics, Geometry / Topology

This book present the topology of smooth 4-manifolds in an intuitive self-contained way. The handlebody theory, and the seiberg-witten theory of 4-manifolds are presented. Also stein and symplectic ... More


The knowledge–power knot in professionalism: transforming the ‘currency of competition’

Ellen Kuhlmann

in Modernising health care: Reinventing professions, the state and the public

Published in print:
2006
Published Online:
March 2012
ISBN:
9781861348586
eISBN:
9781447302810
Item type:
chapter
Publisher:
Policy Press
DOI:
10.1332/policypress/9781861348586.003.0010
Subject:
Public Health and Epidemiology, Public Health

This chapter examines the knowledge-power knot of professionalism. The power of biomedical knowledge is not simply changed through standardisation and EBM. Moreover, ambivalence is embedded in ... More


Other Minds

Sergio Balari and Guillermo Lorenzo

in Computational Phenotypes: Towards an Evolutionary Developmental Biolinguistics

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199665464
eISBN:
9780191746116
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199665464.003.0007
Subject:
Linguistics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics, Historical Linguistics

This chapter defends the proposition that minds other than human are probably endowed with a system of computation homologous to that of FL in terms of computational complexity. It defends the idea ... More


At the Crossroads: The Intercession of Diaghilev

Charles M. Joseph

in Stravinsky and Balanchine: A Journey of Invention

Published in print:
2002
Published Online:
October 2013
ISBN:
9780300087123
eISBN:
9780300129342
Item type:
chapter
Publisher:
Yale University Press
DOI:
10.12987/yale/9780300087123.003.0002
Subject:
Society and Culture, Cultural Studies

This chapter talks about Serge Pavlovich Diaghilev—a figure who stands at the intersection of the Stravinsky-Balanchine union. In retracing the origins of the composer and choreographer's ... More


Braids

Aaron Abrams

in Office Hours with a Geometric Group Theorist

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691158662
eISBN:
9781400885398
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691158662.003.0018
Subject:
Mathematics, Geometry / Topology

This chapter deals with mathematical braids, an idealized abstraction of the familiar hair and bread braids. In a mathematical braid, the “strings” remain separate at the ends rather than being fused ... More


Two Lectures on the Jones Polynomial and Khovanov Homology

Edward Witten

in Lectures on Geometry

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198784913
eISBN:
9780191827150
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198784913.003.0001
Subject:
Mathematics, Geometry / Topology

In the first of these two lectures I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable q. The two main steps are to reinterpret ... More


Elementary Knot Theory

Marc Lackenby

in Lectures on Geometry

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198784913
eISBN:
9780191827150
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198784913.003.0002
Subject:
Mathematics, Geometry / Topology

This is an elementary survey of knot theory. It is a well developed, but there remain several notoriously intractable problems about knots and links, many of which are surprisingly easy to state. The ... More


Path Components and the Fundamental Group

Graham Ellis

in An Invitation to Computational Homotopy

Published in print:
2019
Published Online:
November 2019
ISBN:
9780198832973
eISBN:
9780191871375
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198832973.003.0001
Subject:
Mathematics, Computational Mathematics / Optimization, Geometry / Topology

This chapter introduces some of the basic concepts of algebraic topology and describes datatypes and algorithms for implementing them on a computer. The basic concepts include: regular CW-complex, ... More


Needles in a Haystack: the Class NP

Cristopher Moore and Stephan Mertens

in The Nature of Computation

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199233212
eISBN:
9780191775079
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199233212.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

NP refers to a class of decision problems in which yes-instances are easy to verify. That is: a decision problem is in NP if, whenever the answer for a particular instance is ‘yes’, there is a simple ... More


For Tying Knots: Who invented language and mathematics?

Vinciane Despret

in What Would Animals Say If We Asked the Right Questions?

Published in print:
2016
Published Online:
January 2017
ISBN:
9780816692378
eISBN:
9781452954394
Item type:
chapter
Publisher:
University of Minnesota Press
DOI:
10.5749/minnesota/9780816692378.003.0020
Subject:
Philosophy, General

This chapter explores animals’ capacity for mathematics, arithmetic, and recognizing numerical difference, whether through cognitive ability or gestalt sensing. In an analysis of a knot-tying ape, ... More


Lattice Models of Linear and Ring Polymers

E.J. Janse Van Rensburg

in The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

Published in print:
2015
Published Online:
August 2015
ISBN:
9780199666577
eISBN:
9780191748653
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199666577.003.0001
Subject:
Mathematics, Mathematical Physics

In Chapter 1 the self-avoiding walk connective constant, growth constant and subadditivity are introduced. Concatenation and the supermultiplicativity of lattice polygons are discussed. Scaling, ... More


Self-avoiding walks and polygons

E.J. Janse Van Rensburg

in The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

Published in print:
2015
Published Online:
August 2015
ISBN:
9780199666577
eISBN:
9780191748653
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199666577.003.0007
Subject:
Mathematics, Mathematical Physics

Chapter 7 provides an overview of self-avoiding walks, polygons and half-space walks. The Hammersley-Welsh construction is discussed, as well as the bridge decomposition of half-space walks. Loops, ... More


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