Related papers: A Note on Semidensities in Antisymplectic Geometry

The moduli space of spatial polygons is known as a symplectic manifold equipped with both K\"ahler and real polarizations. In this paper, associated to the K\"ahler and real polarizations, morphisms of operads…

This is a copy of the article published in IMRN (2007). I describe the noncommutative Batalin-Vilkovisky geometry associated naturally with arbitrary modular operad. The classical limit of this geometry is the noncommutative symplectic…

Into a geometric setting, we import the physical interpretation of index theorems via semi-classical analysis in topological quantum field theory. We develop a direct relationship between Fedosov's deformation quantization of a symplectic…

Selfadjoint and maximal dissipative extensions of a non-densely defined symmetric operator $S$ in an infinite-dimensional separable Hilbert space are considered and their compressions on the subspace ${\rm \overline{dom}\,} S$ are studied.…

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 exact sequence induced by a global section using…

We consider non-self-adjoint Schr\"odinger operators $\Delta+V$ where $\Delta$ is the Laplace-Beltrami operator on a Zoll manifold $X$ and $V\in C^\infty(X,\mathbb C)$. We obtain asymptotic results on the pseudo-spectrum and numerical range…

We define an $S^1$-equivariant index for non-compact symplectic manifolds with Hamiltonian $S^1$-action. We use the perturbation by Dirac-type operator along the $S^1$-orbits. We give a formulation and a proof of quantization conjecture for…

In this article, we geometrically study the partial Bernstein-Zelevinsky operator introduced in the author's thesis, which generalizes the original Bernstein-Zelevinsky operator. We relate the partial Bernstein-Zelevinsky operator to the…

We present a generalization of the perturbative construction of the metric operator for non-Hermitian Hamiltonians with more than one perturbation parameter. We use this method to study the non-Hermitian scattering Hamiltonian:…

We classify the connected pseudo-Riemannian manifolds of signature $(p,q)$ with $q\ge5$ so that at each point of $M$ the skew-symmetric curvature operator has constant rank 2 and constant Jordan normal form on the set of spacelike 2 planes…

We construct quasimodes for some non-selfadjoint semiclassical operators at the boundary of the pseudo-spectrum using propagation of Hagedorn wave-packets. Assuming that the imaginary part of the principal symbol of the operator is…

A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…

We study the questions of uniqueness and non-uniqueness for a pair of closely related inverse problems for the Bakry-\'Emery Laplacian $-\Delta_{\mathcal E}$ on a smooth compact and oriented Riemannian manifold with boundary…

We obtain a standard local presentation for a vector-valued multisymplectic form on a smooth manifold, generalizing the known proof for polysymplectic forms. We show that vector-valued multisymplectic forms on a finite-dimensional real…

We study the general geometrical structure of the coadjoint orbits of a semidirect product formed by a Lie group and a representation of this group on a vector space. The use of symplectic induction methods gives new insight into the…

The authors define a class of functions on Riemannian manifolds, which is called geodesic semilocal E-preinvex functions, as a generalization of geodesic semilocal E-convex and geodesic semi E-preinvex functions and some of its properties…

We establish conditions for which graph Laplacians $\Delta_{\lambda,\epsilon}$ on compact, boundaryless, smooth submanifolds $\mathcal{M}$ of Euclidean space are semiclassical pseudodifferential operators ($\Psi$DOs): essentially, that the…

Moduli spaces of polygons have been studied since the nineties for their topological and symplectic properties. Under generic assumptions, these are symplectic manifolds with natural global action-angle coordinates. This paper is concerned…

We give a Riemannian structure to the set $\Sigma$ of positive invertible unitized Hilbert-Schmidt operators, by means of the trace inner product. This metric makes of $\Sigma$ a nonpositively curved, simply connected and metrically…

We use algebras of pseudodifferential operators on groupoids to study geometric operators on non-compact manifolds and singular spaces. The first step is to establish that the geometric operators are in our algebras. This then leads to…