9 papers
The universal moduli space of non-degenerate harmonic spinors
Siqi He, Gregory J. Parker, Thomas Walpuski
This article equips the universal moduli spaces of non-degenerate harmonic spinors and eigenspinors with tame Fréchet manifold structures and proves that t…
Calabi surgery for Z/2 harmonic 1-forms
Jiahuang Chen, Siqi He, Dashen Yan
We prove a 2-valued analogue of Calabi's intrinsic harmonicity theorem and use it to introduce the Calabi surgery method, a surgery theory for harmonic -forms. On…
Deformation rigidity for Z/2 eigensections
Andriy Haydys, Siqi He, Willem Adriaan Salm
We prove a rigidity result for certain critical Z/2 eigensections of the Laplacian on S^2 associated to a flat real line bundle determined by a branch-point configuration. More pre…
Metric perturbations and deformations of k-nondegenerate Z/2-harmonic 1-forms
Siqi He, Willem Adriaan Salm
We study metric perturbations and deformation theory for degenerate Z/2-harmonic 1-forms. For a natural class of degenerate examples, we prove that after a suitable perturbation of…
On the non-Archimedean Hitchin map for
Jiahuang Chen, Siqi He
Let be a non-Archimedean valued field, a closed Riemann surface of genus at least two, and its fundamental group. Building on the theory of equivariant harmonic maps in…
The asymptotics of the -Hitchin metric on the singular locus: subintegrable systems
Siqi He, Johannes Horn, Nianzi Li
We study the asymptotic hyperkähler geometry of the -Hitchin moduli space over the singular fibers of the Hitchin fibration. We extend the previously kno…
Z/2 harmonic 1-forms, R-trees, and the Morgan-Shalen compactification
Siqi He, Richard Wentworth, Boyu Zhang
This paper studies the relationship between an analytic compactification of the moduli space of flat connections on a closed, oriented 3-manifold de…
-Harmonic Spinors and 1-forms on Connected sums and Torus sums of 3-manifolds
Siqi He, Gregory J. Parker
Given a pair of -harmonic spinors (resp. 1-forms) on closed Riemannian 3-manifolds and , we construct -harmonic spinors (resp. 1…
On the existence and rigidity of critical Z2 eigenvalues
Jiahuang Chen, Siqi He
In this article, we study the eigenvalues and eigenfunction problems for the Laplace operator on multivalued functions, defined on the complement of the 2n points on the round sphe…