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Hardcover ISBN:  9780821844304 
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AMS Member Price:  $219.20 $165.20 
Hardcover ISBN:  9780821844304 
Product Code:  PSPUM/78 
List Price:  $139.00 
MAA Member Price:  $125.10 
AMS Member Price:  $111.20 
eBook ISBN:  9780821893852 
Product Code:  PSPUM/78.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Hardcover ISBN:  9780821844304 
eBook ISBN:  9780821893852 
Product Code:  PSPUM/78.B 
List Price:  $274.00 $206.50 
MAA Member Price:  $246.60 $185.85 
AMS Member Price:  $219.20 $165.20 

Book DetailsProceedings of Symposia in Pure MathematicsVolume: 78; 2008; 304 ppMSC: Primary 14; 53; 81
Ideas from quantum field theory and string theory have had an enormous impact on geometry over the last two decades. One extremely fruitful source of new mathematical ideas goes back to the works of Cecotti, Vafa, et al. around 1991 on the geometry of topological field theory. Their tt*geometry (tt* stands for topologicalantitopological) was motivated by physics, but it turned out to unify ideas from such separate branches of mathematics as singularity theory, Hodge theory, integrable systems, matrix models, and Hurwitz spaces. The interaction among these fields suggested by tt*geometry has become a fast moving and exciting research area.
This book, loosely based on the 2007 Augsburg, Germany workshop "From tQFT to tt* and Integrability", is the perfect introduction to the range of mathematical topics relevant to tt*geometry. It begins with several surveys of the main features of tt*geometry, Frobenius manifolds, twistors, and related structures in algebraic and differential geometry, each starting from basic definitions and leading to current research. The volume moves on to explorations of current foundational issues in Hodge theory: higher weight phenomena in twistor theory and noncommutative Hodge structures and their relation to mirror symmetry. The book concludes with a series of applications to integrable systems and enumerative geometry, exploring further extensions and connections to physics.
With its progression through introductory, foundational, and exploratory material, this book is an indispensable companion for anyone working in the subject or wishing to enter it.
ReadershipGraduate students and research mathematicians interested in mathematical physics.

Table of Contents

Articles

Claude Sabbah — Universal unfoldings of Laurent polynomials and $tt^*$ structures [ MR 2483791 ]

Kyoji Saito and Atsushi Takahashi — From primitive forms to Frobenius manifolds [ MR 2483747 ]

Claus Hertling and Christian Sevenheck — Twistor structures, $tt^*$geometry and singularity theory [ MR 2483748 ]

Vicente Cortés and Lars Schäfer — Differential geometric aspects of the $\mathrm {tt}^*$equations [ MR 2483749 ]

L. Katzarkov, M. Kontsevich and T. Pantev — Hodge theoretic aspects of mirror symmetry [ MR 2483750 ]

Carlos Simpson — A weight two phenomenon for the moduli of rank one local systems on open varieties [ MR 2483751 ]

L. K. Hoevenaars — Associativity for the Neumann system [ MR 2483752 ]

Anton A. Gerasimov and Samson L. Shatashvili — Twodimensional gauge theories and quantum integrable systems [ MR 2483753 ]

Vincent Bouchard and Marcos Mariño — Hurwitz numbers, matrix models and enumerative geometry [ MR 2483754 ]

Andrew Neitzke and Johannes Walcher — Background independence and the open topological string wavefunction [ MR 2483755 ]


Additional Material

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Ideas from quantum field theory and string theory have had an enormous impact on geometry over the last two decades. One extremely fruitful source of new mathematical ideas goes back to the works of Cecotti, Vafa, et al. around 1991 on the geometry of topological field theory. Their tt*geometry (tt* stands for topologicalantitopological) was motivated by physics, but it turned out to unify ideas from such separate branches of mathematics as singularity theory, Hodge theory, integrable systems, matrix models, and Hurwitz spaces. The interaction among these fields suggested by tt*geometry has become a fast moving and exciting research area.
This book, loosely based on the 2007 Augsburg, Germany workshop "From tQFT to tt* and Integrability", is the perfect introduction to the range of mathematical topics relevant to tt*geometry. It begins with several surveys of the main features of tt*geometry, Frobenius manifolds, twistors, and related structures in algebraic and differential geometry, each starting from basic definitions and leading to current research. The volume moves on to explorations of current foundational issues in Hodge theory: higher weight phenomena in twistor theory and noncommutative Hodge structures and their relation to mirror symmetry. The book concludes with a series of applications to integrable systems and enumerative geometry, exploring further extensions and connections to physics.
With its progression through introductory, foundational, and exploratory material, this book is an indispensable companion for anyone working in the subject or wishing to enter it.
Graduate students and research mathematicians interested in mathematical physics.

Articles

Claude Sabbah — Universal unfoldings of Laurent polynomials and $tt^*$ structures [ MR 2483791 ]

Kyoji Saito and Atsushi Takahashi — From primitive forms to Frobenius manifolds [ MR 2483747 ]

Claus Hertling and Christian Sevenheck — Twistor structures, $tt^*$geometry and singularity theory [ MR 2483748 ]

Vicente Cortés and Lars Schäfer — Differential geometric aspects of the $\mathrm {tt}^*$equations [ MR 2483749 ]

L. Katzarkov, M. Kontsevich and T. Pantev — Hodge theoretic aspects of mirror symmetry [ MR 2483750 ]

Carlos Simpson — A weight two phenomenon for the moduli of rank one local systems on open varieties [ MR 2483751 ]

L. K. Hoevenaars — Associativity for the Neumann system [ MR 2483752 ]

Anton A. Gerasimov and Samson L. Shatashvili — Twodimensional gauge theories and quantum integrable systems [ MR 2483753 ]

Vincent Bouchard and Marcos Mariño — Hurwitz numbers, matrix models and enumerative geometry [ MR 2483754 ]

Andrew Neitzke and Johannes Walcher — Background independence and the open topological string wavefunction [ MR 2483755 ]