17 citations · 59 across the 12 of their papers we have counts for
14 papers
Inverse spectral results for the magnetic Schrödinger operator in low dimensions
Devon Farrell, Anna Holloway, Nikhil Savale
We consider the semiclassical magnetic Schrödinger operator in dimensions one and two. The first result is that an even one dimensional semiclassical potential is spectrally determ…
The eta invariant of a circle bundle on a Fano manifold
Nikhil Savale
We consider the spin-c Dirac operator on the unit circle bundle of a positive line bundle over a Fano manifold of even complex dimension. We compute the corresponding eta invariant…
Geometric quantization results for semi-positive line bundles on a Riemann surface
George Marinescu, Nikhil Savale
In earlier work the authors proved the Bergman kernel expansion for semipositive line bundles over a Riemann surface whose curvature vanishes to atmost finite order at each point.…
Kähler-Einstein Bergman metrics on pseudoconvex domains of dimension two
Nikhil Savale, Ming Xiao
We prove that a two dimensional pseudoconvex domain of finite type with a Kähler-Einstein Bergman metric is biholomorphic to the unit ball. This answers an old question of Yau for…
Quantitative version of Weyl's law
Nikhil Savale
We prove a general estimate for the Weyl remainder of an elliptic, semiclassical pseudodifferential operator in terms of volumes of recurrence sets for the Hamilton flow of its pri…
Bergman-Szegő kernel asymptotics in weakly pseudoconvex finite type cases
Chin-Yu Hsiao, Nikhil Savale
We construct a pointwise Boutet de Monvel-Sjöstrand parametrix for the Szegő kernel of a weakly pseudoconvex three dimensional CR manifold of finite type assuming the range of its…
Hyperbolicity, irrationality exponents and the eta invariant
Nikhil Savale
We consider the remainder term in the semiclassical limit formula for the eta invariant on a metric contact manifold, proving in general that it is controlled by volumes of recurre…
Spectrum and abnormals in sub-Riemannian geometry: the 4D quasi-contact case
Nikhil Savale
We prove several relations between spectrum and dynamics including wave trace expansion, sharp/improved Weyl laws, propagation of singularities and quantum ergodicity for the sub-R…
Bochner Laplacian and Bergman kernel expansion of semi-positive line bundles on a Riemann surface
George Marinescu, Nikhil Savale
We generalize the results of Montgomery for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel exp…
Sub-leading asymptotics of ECH capacities
Daniel Cristofaro-Gardiner, Nikhil Savale
In previous work, the first author and collaborators showed that the leading asymptotics of the embedded contact homology (ECH) spectrum recovers the contact volume. Our main theor…
A Gutzwiller type trace formula for the magnetic Dirac operator
Nikhil Savale
For manifolds including metric-contact manifolds with non-resonant Reeb ow, we prove a Gutzwiller type trace formula for the associated magnetic Dirac operator involving contributi…
Koszul complexes, Birkhoff normal form and the magnetic Dirac operator
Nikhil Savale
We consider the semi-classical Dirac operator coupled to a magnetic potential on a large class of manifolds including all metric contact manifolds. We prove a sharp local Weyl law…
The Gauss-Bonnet-Chern theorem: a probabilistic perspective
Liviu I. Nicolaescu, Nikhil Savale
We prove that the Euler form of a metric connection on real oriented vector bundle over a compact oriented manifold can be identified, as a current, with the expectation of…
Asymptotics of the eta invariant
Nikhil Savale
We prove an asymptotic bound on the eta invariant of a family of coupled Dirac operators on an odd dimensional manifold. In the case when the manifold is the unit circle bundle of…