Inventiones mathematicae

, Volume 201, Issue 2, pp 711–772 | Cite as

BCFG Drinfeld–Sokolov hierarchies and FJRW-theory

  • Si-Qi Liu
  • Yongbin Ruan
  • Youjin Zhang


In 1991, Witten [ 41] proposed a remarkable conjecture relating the intersection theory of the Deligne–Mumford moduli space \({\overline{\mathcal {M}}}_{g,k}\)



The first and third authors would like to thank Boris Dubrovin for his encouragements and helpful discussions. Part of their work was supported by NSFC No. 11071135, No. 11171176, No. 11222108, and No. 11371214, and by the Marie Curie IRSES project RIMMP. The second author would like to thank his collaborator Todor Milanov from whom he learned most of his knowledge of integrable hierarchies. A special thanks goes to Edward Witten for inspiration and guidance on integrable hierarchies mirror symmetry. His work is partly supported by NSF grant DMS-1103368 and NSF FRG grant DMS-1159265.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingPeople’s Republic of China
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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