Related papers: The spectral Einstein functional for the Witten De…

We classify all self-dual Einstein four-manifolds invariant under a principal action of the three-dimensional Heisenberg group with non-degenerate orbits. The metrics are explicit and we find, in particular, that the Einstein constant can…

Starting with a compact hyperbolic cone-manifold of dimension n > 2, we study the deformations of the metric in order to get Einstein cone-manifolds. If the singular locus is a closed codimension 2 submanifold and all cone angles are…

We study warped products semi-Riemannian Einstein manifolds. We consider the case in that the base is conformal to an n-dimensional pseudo Euclidean space and invariant under the action of an translation group. We provide all such solutions…

Using known mode properties, the functional determinant for massless spin-half fields on the Euclidean 4-ball is calculated and shown to be different for spectral (nonlocal) and mixed (local) boundary conditions. The local result agrees…

Let $M$ be a weighted manifold with boundary $\partial M$, i.e., a Riemannian manifold where a density function is used to weight the Riemannian Hausdorff measures. In this paper we compute the first and the second variational formulas of…

The eigenvalue equation has been found for a Hamilton function in a form independent of the choice of a potential. This paper proposes a modified Fedosov construction on a flat symplectic manifold. Necessary and sufficient conditions for…

We explicitly compute the Green's function of the spinor Klein-Gordon equation on the Riemannian and Lorentzian manifolds of the form $M_0 \times ... \times M_N$, with each factor being a space of constant sectional curvature. Our approach…

We review the role played by tau functions of special type - called {\it Bergman} tau functions in various areas: theory of isomonodromic deformations, solutions of Einstein's equations, theory of Dubrovin-Frobenius manifolds, geometry of…

We compute the nonvanishing spectral torsion functional of the internal part of the noncommutative geometry behind the Standard Model. We show that with a suitable modification of the usual differential graded calculus it matches an…

We study the spectral zeta functions associated to the radial Schr\"odinger problem with potential V(x)=x^{2M}+alpha x^{M-1}+(lambda^2-1/4)/x^2. Using the quantum Wronskian equation, we provide results such as closed-form evaluations for…

We study the Laplacian on Stenzel spaces (generalized deformed conifolds), which are tangent bundles of spheres endowed with Ricci flat metrics. The (2d-2)-dimensional Stenzel space has SO(d) symmetry and can be embedded in C^d through the…

Let $Y$ be a closed and oriented $3$-manifold. We define different versions of unfolded Seiberg-Witten Floer spectra for $Y$. These invariants generalize Manolescu's Seiberg-Witten Floer spectrum for rational homology $3$-spheres. We also…

We explain how to construct a quantum deformation of a spectral curve to a tau-function of the KP hierarchy. This construction is applied to Witten-Kontsevich tau-function to give a natural explanation of some earlier work. We also apply it…

We review two different methods of calculating Witten's invariant: a stationary phase approximation and a surgery calculus. We give a detailed description of the 1-loop approximation formula for Witten's invariant and of the technics…

We perform an unitary transformation for the symmetric phonon mode of the Holstein molecular crystal hamiltonian. We show how to compute the electronic spectral functions by exact numerical diagonalisation of an effective hamiltonian fully…

The thermal Wightman functions for free, massless particles of spin 0, 1/2, 1, 3/2, and 2 are computed directly in coordinate space by solving the appropriate differential equation and imposing the Kubo-Martin-Schwinger condition. The…

We consider almost Einstein solitons $(V,\lambda)$ in a Riemannian manifold when $V$ is a gradient, a solenoidal or a concircular vector field. We explicitly express the function $\lambda$ by means of the gradient vector field $V$ and…

The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection $A$ on a line bundle $L$ and a section $\phi$ of another…

If $M$ is the underlying smooth oriented $4$-manifold of a Del Pezzo surface, we consider the set of Riemannian metrics $h$ on $M$ such that $W^+(\omega , \omega )> 0$, where $W^+$ is the self-dual Weyl curvature of $h$, and $\omega$ is a…

We construct non-trivial continuous isospectral deformations of Riemannian metrics on the ball and on the sphere in $\R^n$ for every $n\geq 9$. The metrics on the sphere can be chosen arbitrarily close to the round metric; in particular,…