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періодичних видань НАН України
періодичних видань НАН України
Integrability, Quantization and Moduli Spaces of Curves
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Integrability, Quantization and Moduli Spaces of Curves
Інший ID:
2010 Mathematics Subject Classification: 14H10; 14H70; 37K10
Посилання:
Integrability, Quantization and Moduli Spaces of Curves / P. Rossi // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 37 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Recent Advances in Quantum Integrable Systems. The
full collection is available at http://www.emis.de/journals/SIGMA/RAQIS2016.html.
This paper originates in part from my Habilitation m´emoire [34] and in part from an introductory talk I gave at the RAQIS’16 conference held at Geneva, Switzerland, in August 2016.
I would like to express my gratitude to its organizers. Moreover I would like to thank my direct collaborators on the DR hierarchy project, A. Buryak, B. Dubrovin and J. Gu´er´e, and the
people who supported us with advice and insight, among the others Dimitri Zvonkine, Rahul
Pandharipande and Yakov Eliashberg. During this work I was partially supported by a Chaire
CNRS/Enseignement superieur 2012–2017 grant.
Дата:
2017
Переглядів:
407
Завантажень:
275
Анотація:
This paper has the purpose of presenting in an organic way a new approach to integrable (1+1)-dimensional field systems and their systematic quantization emerging from intersection theory of the moduli space of stable algebraic curves and, in particular, cohomological field theories, Hodge classes and double ramification cycles. This methods are alternative to the traditional Witten-Kontsevich framework and its generalizations by Dubrovin and Zhang and, among other advantages, have the merit of encompassing quantum integrable systems. Most of this material originates from an ongoing collaboration with A. Buryak, B. Dubrovin and J. Guéré.
