6 papers
Spectral asymmetry, supersymmetry and the equivariant Riemann-Roch defect
Gayana Jayasinghe, Alex R. Taylor, Xinran Yu
We investigate the relationship between two interpretations of equivariant Riemann-Roch defects of complex spaces with conic singularities; as (i) equivariant and i…
Logarithmic wave decay for short range wavespeed perturbations with radial regularity
Gayana Jayasinghe, Katrina Morgan, Jacob Shapiro +1
We establish logarithmic local energy decay for wave equations with a varying wavespeed in dimensions two and higher, where the wavespeed is assumed to be a short range perturbatio…
Supersymmetric harmonic oscillators on singular geometries
Gayana Jayasinghe
Equivariant localization expresses global invariants in terms of local invariants, and many of them appearing in equivariant index theory, (holomorphic) Morse theory, geometric qua…
Witten instanton complex and Morse-Bott inequalities on stratified pseudomanifolds
Gayana Jayasinghe, Hadrian Quan, Xinran Yu
In this paper we construct Witten instanton complexes on stratified pseudomanifolds with wedge metrics, for all choices of mezzo-perversities which classify the self-adjoint extens…
Holomorphic Witten instanton complexes on stratified pseudomanifolds with Kähler wedge metrics
Gayana Jayasinghe
We construct Witten instanton complexes for Kähler Hamiltonian Morse functions on stratified pseudomanifolds with wedge Kähler metrics satisfying a local conformally totally geodes…
An analytic approach to Lefschetz and Morse theory on stratified pseudomanifolds
Gayana Jayasinghe
We develop an analytic framework for Lefschetz fixed point theory and Morse theory for Hilbert complexes on stratified pseudomanifolds. We develop formulas for both global and loca…