152 citations · 375 across the 47 of their papers we have counts for
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Balanced fiber bundles and GKM theory
Victor Guillemin, Silvia Sabatini, Catalin Zara
Let be a torus and a compact manifold. Goresky, Kottwitz, and MacPherson show in \cite{GKM} that if is (what was subsequently called) a GKM manifold, then there exi…
A Fulling-Kuchment theorem for the 1D harmonic oscillator
Victor Guillemin, Hamid Hezari
We prove that there exists a pair of "non-isospectral" 1D semiclassical Schrödinger operators whose spectra agree modulo h^\infty. In particular, all their semiclassical trace inva…
Band invariants for perturbations of the harmonic oscillator
Victor Guillemin, Alejandro Uribe, Zuoqin Wang
We study the direct and inverse spectral problems for semiclassical operators of the form $S = S_0 +\h^2V$, where $S_0 = \frac 12 \Bigl(-\h^2Δ_{\bbR^n} + |x|^2\Bigr)$ is the harmon…
A semiclassical heat trace expansion for the perturbed harmonic oscillator
Victor Guillemin, Alejandro Uribe, Zuoqin Wang
In this paper we study a semiclassical heat trace expansion for perturbations of the harmonic oscillator, by adapting to the semiclassical setting techniques developed by Hitrik an…
Equivariant inverse spectral theory and toric orbifolds
Emily B. Dryden, Victor Guillemin, Rosa Sena-Dias
Let O be a symplectic toric 2n-dimensional orbifold with a fixed T^n-action and with a toric Kahler metric g. We previously explored whether, when O is a manifold, the equivariant…