Landau-Ginzburg/Calabi-Yau correspondence in all genera for
elliptic orbifold projective               
lines -- Yefeng Shen, October 14, 2011

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In this talk, I will explain the reconstruction of
Gromov-Witten invariants for elliptic orbifold projective lines
and the Fan-Jarvis-Ruan-Witten(FJRW) invariants for elliptic
singularities. The convergence of Gromov-Witten potentials and
FJRW potentials follows from the reconstruction. The
Calabi-Yau to Landau-Ginzburg mirror symmetry and
Landau-Ginzburg to Landau-Ginzburg mirror symmetry are verified
for these cases.  Using T. Milanov and Y. Ruan's construction of
global B-model for elliptic singularities, we prove the
Landau-Ginzburg/Calabi-Yau correspondence in all genera for
elliptic orbifold projective lines.  This is joint work with
M. Krawitz.