In this contribution to the proceedings of the 68 Rencontre entre Physiciens Théoriciens et Mathématiciens on Deformation Quantization I shall report on some recent joint work with Henrique Bursztyn on the representation theory of ∗-algebras arising from deformation quantization as I presented this in my talk. 2000 Mathematics Subject Classification: 53D55

Solitons are proposed as the agents of plastic and viscoelastic deformation in aligned polyethylene. Interactions between straight, parallel molecules are mapped rigorously onto the Frenkel-Kontorova model. It is shown that these molecular interactions distribute an applied load between molecules, with a characteristic transfer length equal to the soliton width. Load transfer leads to the intro...

Molecules adsorbed in pores cause elastic deformations of the solid matrix leading to either contraction or swelling of the material. Although experimental manifestation of adsorption-induced deformation in clays, coals, carbons, silicas, and other materials has been known for a long time, a rigorous theoretical description of this phenomenon is lacking. We report the nonlocal density functiona...

We provide the main results of a deformation theory of smooth formal schemes as defined in [2]. Smoothness is defined by the local existence of infinitesimal liftings. Our first result is the existence of an obstruction in a certain Ext group whose vanishing guarantees the existence of global liftings of morphisms. Next, given a smooth morphism f0 : X0 → Y0 of noetherian formal schemes and a cl...

In this work, we show that the eigenvalues of the problem  (∆2 + V (x) + λ)u(x) = 0 x ∈ Ω u(x) = ∆u(x) = 0 x ∈ ∂Ω are generically simple in the set of C4 regular regions of Rn, n ≥ 2. In fact, we prove that there exists a residual set of regions C4 diffeomorphic to a given Ω such that all the eigenvalues for a supported plate equation are simple.