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  1. NTU Theses and Dissertations Repository
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請用此 Handle URI 來引用此文件: http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/10040
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dc.contributor.advisor林惠雯(Hui-Wen Lin)
dc.contributor.authorKuan-Wen Laien
dc.contributor.author賴冠文zh_TW
dc.date.accessioned2021-05-20T20:57:37Z-
dc.date.available2011-07-29
dc.date.available2021-05-20T20:57:37Z-
dc.date.copyright2011-07-29
dc.date.issued2011
dc.date.submitted2011-07-28
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.urihttp://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.abstractIn 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.provenanceMade 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.tableofcontentsAcknowledgments 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.isoen
dc.title射影直線上的Gromov-Witten理論zh_TW
dc.titleThe Gromov-Witten theory of P1en
dc.typeThesis
dc.date.schoolyear99-2
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.keywordELSV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.keywordcompleted cycle,ELSV formula,Gromov-Witten theory,Hurwitz number,infinite wedge representation,shifted symmetric function,τ-function,Toda hierarchy,en
dc.relation.page41
dc.rights.note同意授權(全球公開)
dc.date.accepted2011-07-28
dc.contributor.author-college理學院zh_TW
dc.contributor.author-dept數學研究所zh_TW
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