Related papers: Spectral action in noncommutative geometry and glo…

This paper is the the third part of a series of paper whose aim is to use of the framework of \emph{twisted spectral triples} to study conformal geometry from a noncommutive geometric viewpoint. In this paper we reformulate the inequality…

We discuss an extension to Voiculescu's formula for the quasicentral modulus of a tuple of commuting, self-adjoint operators with spectral measure absolutely continuous with respect to a generalized Hausdorff measure. These Hausdorff…

In complete analogy with the classical case, we define the Chern-Simons action functional in noncommutative geometry and study its properties under gauge transformations. As usual, the latter are related to the connectedness of the group of…

We combine aspects of the theory of motives in algebraic geometry with noncommutative geometry and the classification of factors to obtain a cohomological interpretation of the spectral realization of zeros of $L$-functions. The analogue in…

We study the noncommutative geometry of a two-leaf Parisi--Sourlas supermanifold in Connes' formalism using different $K$-cycles over the Grassmann algebra valued functions on the supermanifold. We find that the curvature of the trivial…

This thesis concerns the research on a Lorentzian generalization of Alain Connes' noncommutative geometry. In the first chapter, we present an introduction to noncommutative geometry within the context of unification theories. The second…

In this paper, we use the language of noncommutative differential geometry to formalise discrete differential calculus. We begin with a brief review of inverse limit of posets as an approximation of topological spaces. We then show how to…

We prove inverse spectral results for differential operators on manifolds and orbifolds invariant under a torus action. These inverse spectral results involve the asymptotic equivariant spectrum, which is the spectrum itself together with…

We compute the super Liouville action for a two dimensional Regge surface by exploiting the invariance of the theory under the superconformal group for sphere topology and under the supermodular group for torus topology. For sphere topology…

We study the noncommutative geometry of the Moyal plane from a metric point of view. Starting from a non compact spectral triple based on the Moyal deformation A of the algebra of Schwartz functions on R^2, we explicitly compute Connes'…

We survey noncommutative spacetimes with coordinates being enveloping algebras of Lie algebras. We also explain how to do differential geometry on noncommutative spaces that are obtained from commutative ones via a Moyal-product type…

We study spectral asymptotics for small non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part possesses several invariant Lagrangian tori…

We rehabilitate the M_1(C)+ M_2(C)+ M_3(C) model of electro-magnetic, weak and strong forces as an almost commutative geometry in the setting of the spectral action.

The spectral shift function of a pair of self-adjoint operators is expressed via an abstract operator valued Titchmarsh--Weyl $m$-function. This general result is applied to different self-adjoint realizations of second-order elliptic…

We define bilinear functionals of vector fields and differential forms, the densities of which yield the metric and Einstein tensors on even-dimensional Riemannian manifolds. We generalise these concepts in non-commutative geometry and, in…

Let a torus $T$ act freely on a closed manifold $M$ of dimension at least two. We demonstrate that, for a generic $T$-invariant Riemannian metric $g$ on $M$, each real $\Delta_g$-eigenspace is an irreducible real representation of $T$ and,…

We study the action functional associated to a smooth Lagrangian function on the cotangent bundle of a manifold, having quadratic growth in the velocities. We show that, although the action functional is in general not twice differentiable…

A conformal immersion of a 2-torus into the 4-sphere is characterized by an auxiliary Riemann surface, its spectral curve. This complex curve encodes the monodromies of a certain Dirac type operator on a quaternionic line bundle associated…

We consider bosons on Euclidean R^4 that are minimally coupled to an external Yang-Mills field. We compute the logarithmically divergent part of the cut-off regularized quantum effective action of this system. We confirm the known result…

We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to polarization spanned by almost-Hamiltonian vector fields of angle variables. The…