Resolution of singularities is one of the central areas of research in Algebraic Geometry. It is a basic prerequisite for the classification of algebraic varieties up to birational equivalence, since it allows to consider only regular varieties. Hironaka’s monumental work [Hi1] gave a non-constructive, existence proof of resolution of singularities over fields of characteristic zero. Constructi...

In this paper, an iterative super-resolution reconstruction method is introduced for license plate recognition. A high-resolution image of the license plate is reconstructed by fusing the information derived from a set of subpixel shifted low-resolution images. The reconstruction problem is formulated as a system of linear equations that is solved by using the simultaneous algebraic reconstruct...

In this work we use a wavelet representation of the Algebraic Radon Transfom for reconstructing an image from its sinogram at a controlled level of resolution.

The courses are: Triviality, Tangency, Transversality, Symmetry, Simplicity, Singularity. These characteristic local plates serve as our invitation to algebraic surfaces and their resolution. Please take a seat.

In [R], Z. Ran gave a canonical construction for the universal deformation of a simple vector bundle using the Jacobi complex of an appropriate differential graded Lie algebra. Independently, H. Esnault and E. Viehweg made a similar construction. Using these tools, we obtain a resolution for the sheaf of differential operators on smooth geometric quotients of free linear actions of algebraic gr...

We study (i) asymptotic behaviour of wild harmonic bundles, (ii) the relation between semisimple meromorphic flat connections and wild harmonic bundles, (iii) the relation between wild harmonic bundles and polarized wild pure twistor D-modules. As an application, we show the hard Lefschetz theorem for algebraic semisimple holonomic D-modules, conjectured by M. Kashiwara. We also study resolutio...

Refinement is a well-known approach for developing correct-byconstruction software. It has been very successful for producing high quality code e.g., as implemented in the B tool. Yet, such refinement techniques are restricted in the sense that they forbid aliasing (and more generally sharing of data-structures), which often happens in usual programming languages. We propose a sound approach fo...