77 citations · 227 across the 16 of their papers we have counts for
18 papers
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…
Search for Z/2 eigenfunctions on the sphere using machine learning
Andriy Haydys, Willem Adriaan Salm
We use machine learning to search for examples of Z/2 eigenfunctions on the 2-sphere. For this we created a multivalued version of a feedforward deep neural network, and we impleme…
An index theorem for Z/2-harmonic spinors branching along a graph
Andriy Haydys, Rafe Mazzeo, Ryosuke Takahashi
We prove an index formula for the Dirac operator acting on two-valued spinors on a -manifold which branch along a smoothly embedded graph , and with respect to a…
New examples of Z/2 harmonic 1-forms and their deformations
Andriy Haydys, Rafe Mazzeo, Ryosuke Takahashi
We collect a number of elementary constructions of harmonic -forms, and of families of these objects. These examples show that the branching set of a harmonic…
Seiberg-Witten monopoles and flat PSL(2;R)-connections
Andriy Haydys
I show that flat PSL(2;R)-connections on three-manifolds satisfying certain 'stability condition' can be interpreted as solutions of the Seiberg-Witten equations with two spinors.…
Introduction to gauge theory
Andriy Haydys
This is lecture notes for a course given at the PCMI Summer School "Quantum Field Theory and Manifold Invariants" (July 1 -- July 5, 2019). I describe basics of gauge-theoretic app…