Topological Recursion and Its Influence in Analysis, Geometry, and Topology (Proceedings of Symposia in Pure Mathematics) - Hardcover

Chiu-chu Melissa Liu; Motohico Mulase

Hardcover

ISBN 10: 1470435411 ISBN 13: 9781470435417

Publisher: American Mathematical Society, 2018

Synopsis

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, Gromov-Witten invariants, the A-polynomials 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 semi-simple 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, Hurwitz-Frobenius manifolds, and ELSV-type formulas.

About this title

About the Author

Edited by Chiu-Chu Melissa Liu: Columbia University, New York, NY, Motohico Mulase: University of California, Davis, Davis, CA

Edition details

• Publisher: American Mathematical Society
• Publication date: 2018
• Language: English
• ISBN 10: 1470435411
• ISBN 13: 9781470435417
• Binding: Hardcover
• Number of pages: 549
• Editor: Chiu-chu Melissa Liu, Motohico Mulase