V. Mathai

We experimentally investigate the effect of geometrical anisotropy for buoyant ellipsoidal particles rising in a still fluid. All other parameters, such as the Galileo number $Ga \approx 6000$ and the particle density ratio $\Gamma \approx…

For a finite rank projective bundle over a compact manifold, so associated to a torsion, Dixmier-Douady, 3-class, w, on the manifold, we define the ring of differential operators `acting on sections of the projective bundle' in a formal…

Using our earlier proposal for Ramond-Ramond fields in an H-flux on loop space, we extend the Hori isomorphism of Bouwknegt-Evslin-Mathai from invariant differential forms, to invariant exotic differential forms such that the momentum and…

We introduce spherical T-duality, which relates pairs of the form $(P,H)$ consisting of a principal $SU(2)$-bundle $P\rightarrow M$ and a 7-cocycle $H$ on $P$. Intuitively spherical T-duality exchanges $H$ with the second Chern class…

In this note we propose that D-brane charges, in the presence of a topologically non-trivial B-field, are classified by the K-theory of an infinite dimensional C^*-algebra. In the case of B-fields whose curvature is pure torsion our…

In this paper, we suggest a construction of determinant lines of finitely generated Hilbertian modules over finite von Neumann algebras. Nonzero elements of the determinant lines can be viewed as volume forms on the Hilbertian modules.…

In this paper, we initiate the study of nonassociative strict deformation quantization of C*-algebras with a torus action. We shall also present a definition of nonassociative principal torus bundles, and give a classification of these as…

In this paper, we use the parametrised strict deformation quantization of C*-bundles obtained in a previous paper, and give more examples and applications of this theory. In particular, it is used here to classify H_3-twisted noncommutative…

We define and systematically study nonassociative C*-algebras as C*-algebras internal to a topological tensor category. We also offer a concrete approach to these C*-algebras, as G-invariant, norm closed *-subalgebras of bounded operators…

An index theory for projective families of elliptic pseudodifferential operators is developed when the twisting, i.e. Dixmier-Douady, class is decomposable. One of the features of this special case is that the corresponding Azumaya bundle…

T-duality acts on circle bundles by exchanging the first Chern class with the fiberwise integral of the H-flux, as we motivate using E_8 and also using S-duality. We present known and new examples including NS5-branes, nilmanifolds, Lens…

In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of D-brane charges in non-trivial…

In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of…

We present a new categorical classification framework for D-brane charges on noncommutative manifolds using methods of bivariant K-theory. We describe several applications including an explicit formula for D-brane charge in cyclic homology,…

In this note the fractional analytic index, for a projective elliptic operator associated to an Azumaya bundle, of DG/0402329 is related to the equivariant index of Atiyah and Singer for an associated transversally elliptic operator.

We study both the continuous model and the discrete model of the integer quantum Hall effect on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper [CHMM]. Here we model impurities, that is we…

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L^2 torsions which, unlike the work of…

Let $\Qbar$ denote the field of complex algebraic numbers. A discrete group $G$ is said to have the $\sigma$-multiplier algebraic eigenvalue property, if for every matrix $A$ with entries in the twisted group ring over the complex algebraic…

In this paper, we study a refined L2 version of the semiclassical approximation of projectively invariant elliptic operators with invariant Morse type potentials on covering spaces of compact manifolds. We work on the level of spectral…

In this paper, we study an L2 version of the semiclassical approximation of magnetic Schroedinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence…