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The Laplace Operator
This chapter introduces the Laplacian on a smooth compact manifold without boundary and motivates the study of its eigenfunctions through...
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Bootstrap bounds on closed hyperbolic manifolds
The eigenvalues of the Laplace-Beltrami operator and the integrals of products of eigenfunctions must satisfy certain consistency conditions on...
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On the associativity of 1-loop corrections to the celestial operator product in gravity
The question of whether the holomorphic collinear singularities of graviton amplitudes define a consistent chiral algebra has garnered much recent...
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The E10 Wheeler-DeWitt operator at low levels
We consider the Wheeler-DeWitt operator associated with the bosonic part of the Hamiltonian of D = 11 supergravity in a formulation with only the...
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Local Hölder Stability in the Inverse Steklov and Calderón Problems for Radial Schrödinger Operators and Quantified Resonances
We obtain Hölder stability estimates for the inverse Steklov and Calderón problems for Schrödinger operators corresponding to a special class of
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Constructing Hermitian Hamiltonians for spin zero neutral and charged particles on a curved surface: physical approach
The Hamiltonians for a spin zero neutral particle and a charged particle in an electromagnetic field pinned to an arbitrary 2D surface embedded in 3D...
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Diffusion coefficients and MSD measurements on curved membranes and porous media
AbstractWe study some geometric aspects that influence the transport properties of particles that diffuse on curved surfaces. We compare different...
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Geometry and quasiclassical quantization of magnetic monopoles
AbstractWe present the basic physical and mathematical ideas (P. Curie, Darboux, Poincaré, Dirac) that led to the concept of magnetic charge, the...
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The fuzzy BTZ
We introduce a model of a noncommutative BTZ black hole, obtained by quantisation of Poincaré coordinates together with a moving frame. The fuzzy BTZ...
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Bootstrap** closed hyperbolic surfaces
The eigenvalues of the Laplace-Beltrami operator and the integrals of products of eigenfunctions and holomorphic s -differentials satisfy certain...
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A geometric approach to the Yang-Mills mass gap
I provide a new idea based on geometric analysis to obtain a positive mass gap in pure non-abelian renormalizable Yang-Mills theory. The orbit space,...
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Color confinement at the boundary of the conformally compactified AdS5
The topology of closed manifolds forces interacting charges to appear in pairs. We take advantage of this property in the setting of the conformal...
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Stratospheric Planetary Flows from the Perspective of the Euler Equation on a Rotating Sphere
This article is devoted to stationary solutions of Euler’s equation on a rotating sphere, and to their relevance to the dynamics of stratospheric...
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Navier-Stokes Equations
The choice of independent variables called spatial/Eulerian and material/Lagrangean description is explained and the incompressible and compressible...
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Harmonic functions and gravity localization
In models with extra dimensions, matter particles can be easily localized to a ‘brane world’, but gravitational attraction tends to spread out in the...
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Notes on gauge fields and discrete series representations in de Sitter spacetimes
In this note we discuss features of the simplest spinning Discrete Series Unitary Irreducible Representations (UIR) of SO(1,4). These representations...