8 citations · 28 across the 13 of their papers we have counts for
13 papers
Modular interpretation of the Weil-Petersson metric asymptotics for abelian varieties
Yanbo Fang, Andres Gomez
As a first step towards a refined description of the asymptotic of the Weil-Petersson metric on the moduli space of polarized Calabi-Yau manifolds we investigate the concrete case…
Metrized ample line bundles in non-Archimedean geometry II
Yanbo Fang
We introduce a class of semipositive metrics on ample line bundles in non-Archimedean geometry, called Shilov finite metrics. We calculate the determinant metric distorsion in the…
Surface plasmons in metamaterial cavities
Yan-Long Fang, Jeffrey Galkowski
We study scattering by metamaterials with negative indices of refraction, which are known to support \emph{surface plasmons} -- long-lived states that are highly localized at the b…
Critical Fubini-Study metrics over non-archimedean fields
Yanbo Fang
Over a non-archimedean local place, the height of a projective variety with respect to a very ample line bundle equipped with a Fubini-Study metric is related to the naive height o…
On the non-archimedean Monge-Ampère equation in mixed characteristic
Yanbo Fang, Walter Gubler, Klaus Künnemann
Let X be a smooth projective variety over a complete discretely valued field of mixed characteristic. We solve non-archimedean Monge-Ampère equations on X assuming resolution and e…
A mathematical analysis of Casimir interactions I: The scalar field
Yan-Long Fang, Alexander Strohmaier
Starting from the construction of the free quantum scalar field of mass we give mathematically precise and rigorous versions of three different approaches to computing th…
Trace singularities in obstacle scattering and the Poisson relation for the relative trace
Yan-Long Fang, Alexander Strohmaier
We consider the case of scattering of several obstacles in for for the Laplace operator with Dirichlet boundary conditions imposed on the obstacles. I…
Minimizing minor embedding energy: an application in quantum annealing
Yan-Long Fang, P. A. Warburton
A significant challenge in quantum annealing is to map a real-world problem onto a hardware graph of limited connectivity. If the maximum degree of the problem graph exceeds the ma…
Non-Archimedean metric extension for semipositive line bundles
Yanbo Fang
For a projective variety defined over a non-Archimedean complete non-trivially valued field , and a semipositive metrized line bundle over it, we establish a metric…
Analytic definition of spin structure
Zhirayr Avetisyan, Yan-Long Fang, Nikolai Saveliev +1
We work on a parallelizable time-orientable Lorentzian 4-manifold and prove that in this case the notion of spin structure can be equivalently defined in a purely analytic fashion.…
Spectral analysis of the Dirac operator on a 3-sphere
Yan-Long Fang, Michael Levitin, Dmitri Vassiliev
We study the (massless) Dirac operator on a 3-sphere equipped with Riemannian metric. For the standard metric the spectrum is known. In particular, the eigenvalues closest to zero…
Spectral asymptotics for first order systems
Zhirayr Avetisyan, Yan-Long Fang, Dmitri Vassiliev
This is a review paper outlining recent progress in the spectral analysis of first order systems. We work on a closed manifold and study an elliptic self-adjoint first order system…
Analysis as a source of geometry: a non-geometric representation of the Dirac equation
Yan-Long Fang, Dmitri Vassiliev
Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine…