53 citations · 500 across the 103 of their papers we have counts for
6 papers · 1 filter
Open Orbits and Augmentations of Dynkin Diagrams
Sin Tsun Edward Fan, Naichung Conan Leung
Given any representation V of a complex linear reductive Lie group G_0, we show that a larger semi-simple Lie group G with g=g_0 + V + V* + ..., exists precisely when V has a finit…
Gromov-Witten invariants for G/B and Pontryagin product for ΩK
Naichung Conan Leung, Changzheng Li
We give an explicit formula for (T-equivariant) 3-pointed genus zero Gromov-Witten invariants for G/B. We derive it by finding an explicit formula for the equivariant Pontryagin pr…
Hard Lefschetz actions in Riemannian geometry with special holonomy
Naichung Conan Leung, Changzheng Li
It is known that the hard Lefschetz action, together with Kähler identities for Kähler (resp. hyperkähler) manifolds, determines a (resp. $\mathfrak{sp}(…
On SYZ mirror transformations
Kwokwai Chan, Naichung Conan Leung
In this expository paper, we discuss how Fourier-Mukai-type transformations, which we call SYZ mirror transformations, can be applied to provide a geometric understanding of the mi…
Calabi-Yau components in general type hypersurfaces
Naichung Conan Leung, Tom Y. H. Wan
For a one-parameter family of general type hypersurfaces with bases of holomorphic n-forms, we construct open covers using tropical geometry. We show that after normalization, each…
Mirror symmetry for toric Fano manifolds via SYZ transformations
Kwokwai Chan, Naichung Conan Leung
We construct and apply Strominger-Yau-Zaslow mirror transformations to understand the geometry of the mirror symmetry between toric Fano manifolds and Landau-Ginzburg models.