Book Review: Inverse spectral theory

Inverse Spectral Theory for One

Book Review: Contemporary Sensorimotor Theory

Consciousness, with its irreducible subjective character, was almost exclusively a philosophical topic until relatively recently. Today, however, the problem of explaining the felt quality of experience has also become relevant to science and engineering, including robotics andAI: “What would we have to build into a robot so that it really felt the touch of a finger, the redness of red, or the ...

New Approach to Inverse Spectral Theory

Equivariant inverse spectral theory and toric orbifolds

Let O be a symplectic toric orbifold with a fixed T-action and with a toric Kähler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace operator ∆g on C∞(O) determines the moment polytope of O, and hence by Delzant’s theorem determines O up to symplectomorphism. In the setting of toric orbifolds we significantly improve upon our previous results a...

Symplectic inverse spectral theory for pseudodifferential operators

We prove, under some generic assumptions, that the semiclassical spectrum modulo O(~) of a one dimensional pseudodifferential operator completely determines the symplectic geometry of the underlying classical system. In particular, the spectrum determines the hamiltonian dynamics of the principal symbol.