Integrability, Quantization and Moduli Spaces of Curves
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 a...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148729 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Integrability, Quantization and Moduli Spaces of Curves / P. Rossi // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 37 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862597196707266560 |
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| author | Rossi, P. |
| author_facet | Rossi, P. |
| citation_txt | Integrability, Quantization and Moduli Spaces of Curves / P. Rossi // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 37 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-11-27T17:06:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148729 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| isbn | DOI:10.3842/SIGMA.2017.060 |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-27T17:06:45Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Rossi, P. 2019-02-18T18:14:12Z 2019-02-18T18:14:12Z 2017 Integrability, Quantization and Moduli Spaces of Curves / P. Rossi // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 37 назв. — англ. DOI:10.3842/SIGMA.2017.060 1815-0659 2010 Mathematics Subject Classification: 14H10; 14H70; 37K10 https://nasplib.isofts.kiev.ua/handle/123456789/148729 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Integrability, Quantization and Moduli Spaces of Curves Article published earlier |
| spellingShingle | Integrability, Quantization and Moduli Spaces of Curves Rossi, P. |
| title | Integrability, Quantization and Moduli Spaces of Curves |
| title_full | Integrability, Quantization and Moduli Spaces of Curves |
| title_fullStr | Integrability, Quantization and Moduli Spaces of Curves |
| title_full_unstemmed | Integrability, Quantization and Moduli Spaces of Curves |
| title_short | Integrability, Quantization and Moduli Spaces of Curves |
| title_sort | integrability, quantization and moduli spaces of curves |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148729 |
| work_keys_str_mv | AT rossip integrabilityquantizationandmodulispacesofcurves |