{"title":"重构猜想中的图和","authors":"Bohan Fang, Zhengyu Zong","doi":"10.1090/pspum/100/01767","DOIUrl":null,"url":null,"abstract":"The BKMP Remodeling Conjecture \\cite{Ma,BKMP09,BKMP10} predicts all genus open-closed Gromov-Witten invariants for a toric Calabi-Yau $3$-orbifold by Eynard-Orantin's topological recursion \\cite{EO07} on its mirror curve. The proof of the Remodeling Conjecture by the authors \\cite{FLZ1,FLZ3} relies on comparing two Feynman-type graph sums in both A and B-models. In this paper, we will survey these graph sum formulae and discuss their roles in the proof of the conjecture.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Graph sums in the remodeling\\n conjecture\",\"authors\":\"Bohan Fang, Zhengyu Zong\",\"doi\":\"10.1090/pspum/100/01767\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The BKMP Remodeling Conjecture \\\\cite{Ma,BKMP09,BKMP10} predicts all genus open-closed Gromov-Witten invariants for a toric Calabi-Yau $3$-orbifold by Eynard-Orantin's topological recursion \\\\cite{EO07} on its mirror curve. The proof of the Remodeling Conjecture by the authors \\\\cite{FLZ1,FLZ3} relies on comparing two Feynman-type graph sums in both A and B-models. In this paper, we will survey these graph sum formulae and discuss their roles in the proof of the conjecture.\",\"PeriodicalId\":384712,\"journal\":{\"name\":\"Proceedings of Symposia in Pure\\n Mathematics\",\"volume\":\"47 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-11-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of Symposia in Pure\\n Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/pspum/100/01767\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of Symposia in Pure\n Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/pspum/100/01767","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The BKMP Remodeling Conjecture \cite{Ma,BKMP09,BKMP10} predicts all genus open-closed Gromov-Witten invariants for a toric Calabi-Yau $3$-orbifold by Eynard-Orantin's topological recursion \cite{EO07} on its mirror curve. The proof of the Remodeling Conjecture by the authors \cite{FLZ1,FLZ3} relies on comparing two Feynman-type graph sums in both A and B-models. In this paper, we will survey these graph sum formulae and discuss their roles in the proof of the conjecture.
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