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Book DetailsContemporary MathematicsVolume: 541; 2011; 257 ppMSC: Primary 57; 32; 60; 16; 17; 81; 11; 14
This book is based on a 10day workshop given by leading experts in hyperbolic geometry, quantum topology and number theory, in June 2009 at Columbia University. Each speaker gave a minicourse consisting of three or four lectures aimed at graduate students and recent PhDs. The proceedings of this enormously successful workshop can serve as an introduction to this active research area in a way that is expository and broadly accessible to graduate students.
Although many ideas overlap, the twelve expository/research papers in this volume can be grouped into four rough categories:
(1) different approaches to the Volume Conjecture, and relations between the main quantum and geometric invariants;
(2) the geometry associated to triangulations of hyperbolic 3manifolds;
(3) arithmetic invariants of hyperbolic 3manifolds;
(4) quantum invariants associated to knots and hyperbolic 3manifolds.
The workshop, the conference that followed, and these proceedings continue a long tradition in quantum and geometric topology of bringing together ideas from diverse areas of mathematics and physics, and highlights the importance of collaborative research in tackling big problems that require expertise in disparate disciplines.
ReadershipGraduate students and research mathematicians interested in hyperbolic geometry, quantum topology and number theory.

Table of Contents

Articles

Hitoshi Murakami — An introduction to the volume conjecture [ MR 2796626 ]

Tudor Dimofte and Sergei Gukov — Quantum field theory and the volume conjecture [ MR 2796627 ]

R. M. Kashaev — $R$matrix knot invariants and triangulations [ MR 2796628 ]

Stavros Garoufalidis — Knots and tropical curves [ MR 2796629 ]

Stéphane Baseilhac — Quantum coadjoint action and the $6j$symbols of $U_q{\rm sl}_2$ [ MR 2796630 ]

Stavros Garoufalidis — What is a sequence of Nilsson type? [ MR 2796631 ]

David Futer and François Guéritaud — From angled triangulations to hyperbolic structures [ MR 2796632 ]

Feng Luo — Triangulated 3manifolds: from Haken’s normal surfaces to Thurston’s algebraic equation [ MR 2796633 ]

Jessica S. Purcell — An introduction to fully augmented links [ MR 2796634 ]

Genevieve S. Walsh — Orbifolds and commensurability [ MR 2796635 ]

Walter D. Neumann — Realizing arithmetic invariants of hyperbolic 3manifolds [ MR 2796636 ]

D. D. Long and A. W. Reid — Fields of definition of canonical curves [ MR 2796637 ]


Additional Material

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This book is based on a 10day workshop given by leading experts in hyperbolic geometry, quantum topology and number theory, in June 2009 at Columbia University. Each speaker gave a minicourse consisting of three or four lectures aimed at graduate students and recent PhDs. The proceedings of this enormously successful workshop can serve as an introduction to this active research area in a way that is expository and broadly accessible to graduate students.
Although many ideas overlap, the twelve expository/research papers in this volume can be grouped into four rough categories:
(1) different approaches to the Volume Conjecture, and relations between the main quantum and geometric invariants;
(2) the geometry associated to triangulations of hyperbolic 3manifolds;
(3) arithmetic invariants of hyperbolic 3manifolds;
(4) quantum invariants associated to knots and hyperbolic 3manifolds.
The workshop, the conference that followed, and these proceedings continue a long tradition in quantum and geometric topology of bringing together ideas from diverse areas of mathematics and physics, and highlights the importance of collaborative research in tackling big problems that require expertise in disparate disciplines.
Graduate students and research mathematicians interested in hyperbolic geometry, quantum topology and number theory.

Articles

Hitoshi Murakami — An introduction to the volume conjecture [ MR 2796626 ]

Tudor Dimofte and Sergei Gukov — Quantum field theory and the volume conjecture [ MR 2796627 ]

R. M. Kashaev — $R$matrix knot invariants and triangulations [ MR 2796628 ]

Stavros Garoufalidis — Knots and tropical curves [ MR 2796629 ]

Stéphane Baseilhac — Quantum coadjoint action and the $6j$symbols of $U_q{\rm sl}_2$ [ MR 2796630 ]

Stavros Garoufalidis — What is a sequence of Nilsson type? [ MR 2796631 ]

David Futer and François Guéritaud — From angled triangulations to hyperbolic structures [ MR 2796632 ]

Feng Luo — Triangulated 3manifolds: from Haken’s normal surfaces to Thurston’s algebraic equation [ MR 2796633 ]

Jessica S. Purcell — An introduction to fully augmented links [ MR 2796634 ]

Genevieve S. Walsh — Orbifolds and commensurability [ MR 2796635 ]

Walter D. Neumann — Realizing arithmetic invariants of hyperbolic 3manifolds [ MR 2796636 ]

D. D. Long and A. W. Reid — Fields of definition of canonical curves [ MR 2796637 ]