Author

Shing-Tung Yau

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Preprint Aug 2026

A Sharp Curvature Threshold for GLMY Path Homology

Let $G$ be a finite simple graph with at least one edge. We prove the sharp vanishing theorem \[ \kappa_{\min}^{\mathrm{LLY}}(G)>\frac12 \quad\Longrightarrow\quad \PathH_1(G;\R)=0. \] Equivalently, nonzero first GLMY path homology forces an edge of Lin--Lu--Yau curvature at most $1/2$. The threshold $1/2$ is sharp and...

Shu-Liang Bai, Jing-Yan Li, Shing-Tung Yau · 0 citations

Preprint Oct 2026

Stability of the Cotangent Bundle on Surfaces with Ample Canonical Class

In this article, we study the Bridgeland stability of the cotangent bundle on K3 surfaces and surfaces with ample canonical class. On a surface $X$ with ample canonical class $K$, we find values $t_0>0$ such that the cotangent bundle is semistable with respect to the Bridgeland stability $\sigma_{tK}$ for all $t>t_0$....

Tristan C. Collins, Jason Lo, Yun Shi et al. · 0 citations

#edge computing Preprint Oct 2026

Counting higher-rank sheaves on toric threefolds

We develop an equivariant K-theoretic vertex formalism for a colored, abelianized higher-rank sector on smooth projective toric threefolds $X$. Nonzero first Chern classes are encoded as magnetic fluxes and absorbed into line-bundle twists, after which the virtual character is redistributed into finite perturbative, ve...

N. Piazzalunga, A. Sheshmani, Shing-Tung Yau · 0 citations