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Book DetailsProceedings of Symposia in Pure MathematicsVolume: 100; 2018; 549 ppMSC: Primary 14; 53; 81
This volume contains the proceedings of the 2016 AMS von Neumann Symposium on Topological Recursion and its Influence in Analysis, Geometry, and Topology, which was held from July 4–8, 2016, at the Hilton Charlotte University Place, Charlotte, North Carolina.
The papers contained in the volume present a snapshot of rapid and rich developments in the emerging research field known as topological recursion. It has its origin around 2004 in random matrix theory and also in Mirzakhani's work on the volume of moduli spaces of hyperbolic surfaces.
Topological recursion has played a fundamental role in connecting seemingly unrelated areas of mathematics such as matrix models, enumeration of Hurwitz numbers and Grothendieck's dessins d'enfants, GromovWitten invariants, the Apolynomials and colored polynomial invariants of knots, WKB analysis, and quantization of Hitchin moduli spaces. In addition to establishing these topics, the volume includes survey papers on the most recent key accomplishments: discovery of the unexpected relation to semisimple cohomological field theories and a solution to the remodeling conjecture. It also provides a glimpse into the future research direction; for example, connections with the Airy structures, modular functors, HurwitzFrobenius manifolds, and ELSVtype formulas.
ReadershipGraduate students and researchers interested in topological recursion and its applications in various areas of mathematics.

Table of Contents

Articles

Jørgen Ellegaard Andersen, Gaëtan Borot and Nicolas Orantin — Modular functors, cohomological field theories, and topological recursion

Andrea Brini — On the Gopakumar–Ooguri–Vafa correspondence for Clifford–Klein 3manifolds

Lin Chen — BouchardKlemmMarinoPasquetti conjecture for $\mathbb {C}^3$

Alessandro Chiodo and Jan Nagel — The hybrid Landau–Ginzburg models of Calabi–Yau complete intersections

Paweł Ciosmak, Leszek Hadasz, Masahide Manabe and Piotr Sułkowski — Singular vector structure of quantum curves

Norman Do and Maksim Karev — Towards the topological recursion for double Hurwitz numbers

Olivia Dumitrescu and Motohico Mulase — Quantization of spectral curves for meromorphic Higgs bundles through topological recursion

P. DuninBarkowski — Topological recursion and Givental’s formalism: Spectral curves for GromovWitten theories

P. DuninBarkowski, P. Norbury, N. Orantin, A. Popolitov and S. Shadrin — Primary invariants of Hurwitz Frobenius manifolds

João N. Esteves — Hopf algebras and topological recursion

Bohan Fang and Zhengyu Zong — Graph sums in the remodeling conjecture

Taro Kimura — Double quantization of Seiberg–Witten geometry and Walgebras

Maxim Kontsevich and Yan Soibelman — Airy structures and symplectic geometry of topological recursion

D. Korotkin — Periods of meromorphic quadratic differentials and Goldman bracket

D. Lewanski — On ELSVtype formulae, Hurwitz numbers and topological recursion

Xiaojun Liu, Motohico Mulase and Adam Sorkin — Quantum curves for simple Hurwitz numbers of an arbitrary base curve


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This volume contains the proceedings of the 2016 AMS von Neumann Symposium on Topological Recursion and its Influence in Analysis, Geometry, and Topology, which was held from July 4–8, 2016, at the Hilton Charlotte University Place, Charlotte, North Carolina.
The papers contained in the volume present a snapshot of rapid and rich developments in the emerging research field known as topological recursion. It has its origin around 2004 in random matrix theory and also in Mirzakhani's work on the volume of moduli spaces of hyperbolic surfaces.
Topological recursion has played a fundamental role in connecting seemingly unrelated areas of mathematics such as matrix models, enumeration of Hurwitz numbers and Grothendieck's dessins d'enfants, GromovWitten invariants, the Apolynomials and colored polynomial invariants of knots, WKB analysis, and quantization of Hitchin moduli spaces. In addition to establishing these topics, the volume includes survey papers on the most recent key accomplishments: discovery of the unexpected relation to semisimple cohomological field theories and a solution to the remodeling conjecture. It also provides a glimpse into the future research direction; for example, connections with the Airy structures, modular functors, HurwitzFrobenius manifolds, and ELSVtype formulas.
Graduate students and researchers interested in topological recursion and its applications in various areas of mathematics.

Articles

Jørgen Ellegaard Andersen, Gaëtan Borot and Nicolas Orantin — Modular functors, cohomological field theories, and topological recursion

Andrea Brini — On the Gopakumar–Ooguri–Vafa correspondence for Clifford–Klein 3manifolds

Lin Chen — BouchardKlemmMarinoPasquetti conjecture for $\mathbb {C}^3$

Alessandro Chiodo and Jan Nagel — The hybrid Landau–Ginzburg models of Calabi–Yau complete intersections

Paweł Ciosmak, Leszek Hadasz, Masahide Manabe and Piotr Sułkowski — Singular vector structure of quantum curves

Norman Do and Maksim Karev — Towards the topological recursion for double Hurwitz numbers

Olivia Dumitrescu and Motohico Mulase — Quantization of spectral curves for meromorphic Higgs bundles through topological recursion

P. DuninBarkowski — Topological recursion and Givental’s formalism: Spectral curves for GromovWitten theories

P. DuninBarkowski, P. Norbury, N. Orantin, A. Popolitov and S. Shadrin — Primary invariants of Hurwitz Frobenius manifolds

João N. Esteves — Hopf algebras and topological recursion

Bohan Fang and Zhengyu Zong — Graph sums in the remodeling conjecture

Taro Kimura — Double quantization of Seiberg–Witten geometry and Walgebras

Maxim Kontsevich and Yan Soibelman — Airy structures and symplectic geometry of topological recursion

D. Korotkin — Periods of meromorphic quadratic differentials and Goldman bracket

D. Lewanski — On ELSVtype formulae, Hurwitz numbers and topological recursion

Xiaojun Liu, Motohico Mulase and Adam Sorkin — Quantum curves for simple Hurwitz numbers of an arbitrary base curve