12 citations · 13 across the 10 of their papers we have counts for
10 papers
Fermion Families and Pontryagin Class: Topological Field Theory via Colour Symmetry Extension
Zheyan Wan, Juven Wang, Shing-Tung Yau
Family puzzle asks why the Standard Model (SM) features exactly 3 families of quarks and leptons. Motivated by topological constraints, we study 4d fermionic anomalies with discret…
The discrete homotopy hypothesis for directed graphs
Briony Eldridge, Sergei O. Ivanov, Xiaomeng Xu +2
We develop a homotopy theory of directed graphs based on cubical homotopy groups, also known as -groups or reduced GLMY homotopy groups. Localizing the category of directed grap…
Existence of Hermitian metrics with prescribed Hermitian-Yang-Mills tensors II
Jiaxuan Fan, Mingwei Wang, Xiaokui Yang +1
In this paper, we solve the prescribed Hermitian-Yang-Mills tensor problem for Higgs bundles over compact complex manifolds. Let be a Higgs bundle over a compact Hermitia…
Hodge rigidity of Chern classes
Yuxiang Liu, Artan Sheshmani, Shing-Tung Yau
In this paper, we study the homogeneous components of the Chern--Schwartz--MacPherson (CSM) classes of Schubert cells. We prove that, under suitable conditions, each such component…
A Proof of the Eigenvalue Ratio Bound for Embedded Surfaces
Ricardo Gloria-Picazzo, Yingying Wu, Shing-Tung Yau
We explain how the spectrum of a closed embedded surface relates to the Dirichlet spectrum of the bounded domain with $\partial Ω= Σ…
Microlocal index theorems and analytic torsion invariants in the geometric theory of partial differential equations
Jacob Kryczka, Vladimir Rubtsov, Artan Sheshmani +1
We develop a microlocal and derived-geometric framework for index theory and analytic torsion of nonlinear PDEs. By integrating Spencer hypercohomology, microlocal sheaf theory, an…
Algebra of Path Integrals on Digraphs
Shing-Tung Yau, Mengmeng Zhang, Yunpeng Zi
In this paper, we extend the iterated path integrals from smooth manifolds to digraphs and develop the associated algebraic and geometric structures. Iterated path integrals on a d…
Time-dependent Hermite-Galerkin spectral method and its applications
Xue Luo, Shing-Tung Yau, Stephen S. -T. Yau
A time-dependent Hermite-Galerkin spectral method (THGSM) is investigated in this paper for the nonlinear convection-diffusion equations in the unbounded domains. The time-dependen…
Harnack inequalities for graphs with non-negative Ricci curvature
Fan Chung, Yong Lin, Shing-Tung Yau
We establish a Harnack inequality for finite connected graphs with non-negative Ricci curvature. As a consequence, we derive an eigenvalue lower bound, extending previous results f…
A Rigorous Treatment of Energy Extraction from a Rotating Black Hole
Felix Finster, Niky Kamran, Joel Smoller +1
The Cauchy problem is considered for the scalar wave equation in the Kerr geometry. We prove that by choosing a suitable wave packet as initial data, one can extract energy from th…