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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 林惠雯(Hui-Wen Lin) | |
| dc.contributor.author | Kuan-Wen Lai | en |
| dc.contributor.author | 賴冠文 | zh_TW |
| dc.date.accessioned | 2021-05-20T20:57:37Z | - |
| dc.date.available | 2011-07-29 | |
| dc.date.available | 2021-05-20T20:57:37Z | - |
| dc.date.copyright | 2011-07-29 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-07-28 | |
| dc.identifier.citation | [1] T. Ekedahl, S. Lando, M. Shapiro, and A. Vainshtein, Hurwitz numbers and intersections on moduli spaces of curves, Invent. Math. 146 (2001), 297-327.
[2] T. Graber and R. Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999), no. 2, 487V518. [3] P. Johnson, Double Hurwitz numbers via the infinite wedge, arXiv:1008.3266 [4] V. Kac, Infinite dimensional Lie algebras, Cambridge University Press, 1990. [5] S. Kerov and G. Olshanski, Polynomial functions on the set of Young diagrams, C. R. Acad. Sci. Paris Ser. I Math. 319 (1994), no. 2, 121-126. [6] Y.-P. Lee, H.-W. Lin and C.-LWang, Flops, motives, and invariance of quantum rings, Ann. of Math, 172 (2010) no.1 243-290. [7] Y.-P. Lee and R. Pandharipande, A reconstruction theorem in quantum cohomology and quantum K-theory, Amer. J. Math. 126 (2004), no. 6, 1367-1379. [8] T. Miwa, M. Jimbo, and E. Date, Solitons: differential equations, symmetries and infinite dimensional algebras, Translated from the 1993 Japanese original by Miles Reid. Cambridge Tracts in Mathematics, 135. Cambridge University Press, Cambridge, 2000. [9] A. Okounkov, Infinite wedge and random partitions, Selecta Math. (N.S.) 7 (2001), no. 1, 57-81. [10] A. Okounkov and R. Pandharipande, Gromov-Witten theory, Hurwitz numbers, and matrix models, Proc. Sympos. Pure Math., 80, Part 1, 325V414 (2009). [11] A. Okounkov and R. Pandharipande, Gromov-Witten theory, Hurwitz theory, and completed cycles, Ann. of Math. 163 (2006), 517-560. [12] A. Okounkov and R. Pandharipande, The equivariant Gromov-Witten theory of P1, Ann. of Math. 163 (2006), 561-605. [13] S. Shadrin, L. Spitz, D. Zvonkin, On double Hurwitz numbers with completed cycles, arXiv:1103.3120. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/10040 | - |
| dc.description.abstract | 在這篇文章中，我概述了關於Gromov-Witten不變量與Hurwitz數之間如何建立對應的工作，以及詳細探討Toda階序的Hirota方程。該階序能夠提供相當程度的遞迴關係以計算射影直線上的Gromov-Witten不變量。主要的參考文獻為A. Okounkov與R. Pandharipande的一系列論文[11, 12]。 | zh_TW |
| dc.description.abstract | In this article, I would like to outline the work about the correspondence between Gromov-Witten invariants and Hurwitz numbers, and concentrate mainly on the detailed study of Hirota equations for the Toda hierarchy which provides certain recurrence relations for relative Gromov-Witten invariants of P1. The papers of A. Okounkov and R. Pandharipande [11, 12] are the main sources of my study. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T20:57:37Z (GMT). No. of bitstreams: 1 ntu-100-R98221026-1.pdf: 519815 bytes, checksum: ff9932e67496b35f637cf081ad7cc51a (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | Acknowledgments i
Abstract ii Table of contents iii Introduction 1 1. Gromov-Witten invariants and Hurwitz numbers 2 1.1. Gromov-Witten invariants . . . . . . . . . . . . . . . . . . . . . 2 1.2. Hurwitz numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3. Completed cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2. The operator formalism 9 2.1. The Fock representations. . . . . . . . . . . . . . . . . . . . . . 9 2.2. Boson-Fermion correspondence . . . . . . . . . . . . . . . . . 12 2.3. The operators E . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3. The Gromov-Witten/Hurwitz correspondence 18 3.1. Hodge integrals and equivariant n + m-point functions . . 18 3.2. The operator formula for Hodge integrals. . . . . . . . . . . 23 3.3. Special GW/H correspondence. . . . . . . . . . . . . . . . . . 25 3.4. Full GW/H correspondence . . . . . . . . . . . . . . . . . . . . 27 4. Main results 31 4.1. Hirota equations for the Toda hierarchy . . . . . . . . . . . . 32 4.2. The Toda hierarchy in the GW-theory . . . . . . . . . . . . . 33 References 40 | |
| dc.language.iso | en | |
| dc.title | 射影直線上的Gromov-Witten理論 | zh_TW |
| dc.title | The Gromov-Witten theory of P1 | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王金龍(Chin-Lung Wang),李元斌(Yuan-Pin Lee),莊武諺(Wu-Yen Chuang) | |
| dc.subject.keyword | ELSV方程,Gromov-Witten理論,Hurwitz數,τ-函數,Toda階序,完備輪換,偏移對稱函數,無限維楔表示論, | zh_TW |
| dc.subject.keyword | completed cycle,ELSV formula,Gromov-Witten theory,Hurwitz number,infinite wedge representation,shifted symmetric function,τ-function,Toda hierarchy, | en |
| dc.relation.page | 41 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2011-07-28 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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