922 citations · 7.2k across the 348 of their papers we have counts for
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Curvatures of moduli space of curves and applications
Kefeng Liu, Xiaofeng Sun, Xiaokui Yang +1
In this paper, we investigate the geometry of the moduli space of curves by using the curvature properties of direct image sheaves of vector bundles. We show that the moduli space…
An explicit formula of hitting times for random walks on graphs
Hao Xu, Shing-Tung Yau
We prove an explicit formula of hitting times in terms of enumerations of spanning trees for random walks on general connected graphs. We apply the formula to improve Lawler's boun…
Building Blocks for Generalized Heterotic/F-theory Duality
Jonathan J. Heckman, Hai Lin, Shing-Tung Yau
In this note we propose a generalization of heterotic/F-theory duality. We introduce a set of non-compact building blocks which we glue together to reach compact examples of genera…
A mathematical theory of D-string world-sheet instantons, II: Moduli stack of -(semi)stable morphisms from Azumaya nodal curves with a fundamental module to a projective Calabi-Yau 3-fold
Chien-Hao Liu, Shing-Tung Yau
In this Part II, D(10.2), of D(10), we take D(10.1) (arXiv:1302.2054 [math.AG]) as the foundation to define the notion of -semistable morphisms from general Azumaya nodal curves…
Simplicial Ricci Flow: An Example of a Neck Pinch Singularity in 3D
Paul M. Alsing, Warner A. Miller, Matthew Corne +4
We examine a Type-1 neck pinch singularity in simplicial Ricci flow (SRF) for an axisymmetric piecewise flat 3-dimensional geometry with 3-sphere topology. SRF was recently introdu…
A Novel Skew-Hamiltonian Isotropic Lanczos Algorithm for Spectral Conformal Parameterizations
Wei-Qiang Huang, Xianfeng David Gu, Wen-Wei Lin +1
Numerous methods for computing conformal mesh paramterizations has been developed due to the vast applications in the field of geometry processing. Spectral conformal parameterizat…