23 citations · 58 across the 14 of their papers we have counts for
14 papers
Symmetry in Deformation quantization and Geometric quantization
Naichung Conan Leung, Qin Li, Ziming Nikolas Ma
In this paper, we explore the quantization of Kähler manifolds, focusing on the relationship between deformation quantization and geometric quantization. We provide a classificatio…
A perturbative construction of primitive forms from log Landau-Ginzburg mirrors of toric manifolds
Kwokwai Chan, Ziming Nikolas Ma, Hao Wen
We introduce the notion of a logarithmic Landau-Ginzburg (log LG) model, which is essentially given by equipping the central degenerate fiber of the family of Landau-Ginzburg (LG)…
Smoothing, scattering, and a conjecture of Fukaya
Kwokwai Chan, Naichung Conan Leung, Ziming Nikolas Ma
In 2002, Fukaya proposed a remarkable explanation of mirror symmetry detailing the SYZ conjecture by introducing two correspondences: one between the theory of pseudo-holomorphic c…
Geometric quantization and quantum moment maps on coadjoint orbits and Kähler-Einstein manifolds
Naichung Conan Leung, Qin Li, Ziming Nikolas Ma
Deformation quantization and geometric quantization on Kähler manifolds give the mathematical description of the algebra of quantum observables and the Hilbert spaces respectively,…
Tropical Lagrangian multi-sections and smoothing of locally free sheaves over degenerate Calabi-Yau surfaces
Kwokwai Chan, Ziming Nikolas Ma, Yat-Hin Suen
We introduce the notion of tropical Lagrangian multi-sections over a -dimensional integral affine manifold with singularities, and use them to study the reconstruction probl…
Smoothing pairs over degenerate Calabi-Yau varieties
Kwokwai Chan, Ziming Nikolas Ma
We apply the techniques developed in our previous work with Leung to study smoothings of a pair , where is a bounded perfect complex of locally…
Refined scattering diagrams and theta functions from asymptotic analysis of Maurer-Cartan equations
Naichung Conan Leung, Ziming Nikolas Ma, Matthew B. Young
We further develop the asymptotic analytic approach to the study of scattering diagrams. We do so by analyzing the asymptotic behavior of Maurer-Cartan elements of a differential g…
Geometry of the Maurer-Cartan equation near degenerate Calabi-Yau varieties
Kwokwai Chan, Naichung Conan Leung, Ziming Nikolas Ma
Given a degenerate Calabi-Yau variety equipped with local deformation data, we construct an almost differential graded Batalin-Vilkovisky (dgBV) algebra , producin…
Fukaya's conjecture on -equivariant de Rham complex
Ziming Nikolas Ma
Getzler-Jones-Petrack introduced structures on the equivariant complex for manifold with smooth action, motivated by geometry of loop spaces. Applying…
SYZ mirror symmetry from Witten-Morse theory
Ziming Nikolas Ma
This is a survey article on the recent progress in understanding the Strominger-Yau-Zaslow (SYZ) mirror symmetry conjecture, especially on the effect of quantum corrections, via Wi…
Tropical counting from asymptotic analysis on Maurer-Cartan equations
Kwokwai Chan, Ziming Nikolas Ma
Let be a toric surface and be its Landau-Ginzburg (LG) mirror where is the Hori-Vafa potential. We apply asymptotic analysis to study the extended de…
Scattering diagrams from asymptotic analysis on Maurer-Cartan equations
Kwokwai Chan, Naichung Conan Leung, Ziming Nikolas Ma
Let be a semi-flat Calabi-Yau manifold equipped with a Lagrangian torus fibration . We investigate the asymptotic behavior of M…
Fukaya's conjecture on Witten's twisted -structures
Kaileung Chan, Naichung Conan Leung, Ziming Nikolas Ma
Wedge product on deRham complex of a Riemannian manifold can be pulled back to via explicit homotopy, constructed using Green's operator, to give higher product struct…
Lattice point counting via Einstein metrics
Ziming Nikolas Ma, Naichung Conan Leung
We obtain a growth estimate for the number of lattice points inside any Q-Gorenstein cone. Our proof uses the result of Futaki-Ono-Wang on Sasaki-Einstein metric for the toric Sasa…