7 papers
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 Hermiti…
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 referred to as A-groups or reduced GLMY homotopy groups. Localizing the category of directed…
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…
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…