118 citations · 569 across the 39 of their papers we have counts for
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Quantum Hyperplane Section Theorem For Homogeneous Spaces
Bumsig Kim
We formulated a mirror-free approach to the mirror conjecture, namely, quantum hyperplane section conjecture, and proved it in the case of nonnegative complete intersections in hom…
Conifold Transitions and Mirror Symmetry for Calabi-Yau Complete Intersections in Grassmannians
Victor V. Batyrev, Ionunt Ciocan-Fontanine, Bumsig Kim +1
In this paper we show that conifold transitions between Calabi-Yau 3-folds can be used for the construction of mirror manifolds and for the computation of the instanton numbers of…
Quantum cohomology of flag manifolds G/B and quantum Toda lattices
Bumsig Kim
We prove the Givental conjecture that the (equivariant) quantum cohomology of flag manifolds G/B are governed by the conservation law of Toda lattices. In addition, we find the qua…
Quot schemes for flags and Gromov invariants for flag varieties
Bumsig Kim
Using Quot schemes and a localization theorem we study Gromov-Witten invariants for partial flag varieties. The strategy is to extend A. Bertram's result of Gromov-Witten invariant…