Related papers: Jet schemes, arc spaces and the Nash problem
We give a leisurely introduction into mathematical diffraction theory with a focus on pure point diffraction. In particular, we discuss various characterisations of pure point diffraction and common models arising from cut and project…
We use the theory of motivic integration for singular spaces to give a characterization of minimal log discrepencies in terms of the codimension of certain subsets of spaces of arcs. This is done for arbitrary pairs $(X,Y)$, with $X$ normal…
In this brief survey we give an introduction to some aspects of "atoms" on metric spaces and their connection with linear operators.
We find certain relations between flag Hilbert schemes of points on plane curves and moduli spaces of one-dimensional plane sheaves. We show that some of these moduli spaces are unirational.
In this paper we give a positive answer to a question of Nash concerning the arc space of a singularity, for the class of quasi-ordinary hypersurface singularities, extending to this case previous results and techniques of Shihoko Ishii.
The Airy transform is an ideally suited tool to treat problem in classical and quantum optics. Even though the relevant mathematical aspects have been thoroughly investigated, the possibility it offers are wide and some aspects, as the link…
We show that the definition of an algebraic basis for a vector space allows the construction of an isomorphism with the one here called Algebraic Vector Space. Although the concept does not bring anything new, we mention some of the…
This is a list of some problems and conjectures related to various types of algebras, that is to algebraic operads. Some comments and hints are included.
We define and study jets of flat partial connections with respect to singular foliations. In particular, we use the first sheaf of transverse jets to address the problem of extending a flat partial connection to a (flat) meromorphic…
We consider a mechanical system with impact and n degrees of freedom, written in generalized coordinates. The system is not necessarily Lagrangian. The representative point of the system must remain inside a set of constraints K; the…
This paper is a survey of computational issues in algebraic geometry, with particular attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A geometric introduction to Grobner bases. 2. An algebraic…
In this paper, we introduce the category of blueprints, which is a category of algebraic objects that include both commutative (semi)rings and commutative monoids. This generalization allows a simultaneous treatment of ideals resp.\…
In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has…
Jet physics is a rich and rapidly evolving field, with many applications to physics in and beyond the Standard Model. These notes, based on lectures delivered at the June 2012 Theoretical Advanced Study Institute, provide an introduction to…
Airspace sectorisation provides a partition of a given airspace into sectors, subject to geometric constraints and workload constraints, so that some cost metric is minimised. We survey the algorithmic aspects of methods for automatic…
Conventional jet algorithms are based on a deterministic view of the underlying hard scattering process. Each outgoing parton from the hard scattering is associated with a hard, well separated jet. This approach is very successful because…
As an overview of blazar research, we briefly discuss some of the themes of this conference, including the various types of blazars, blazar samples and selection effects, unified schemes, evolution, and jet physics.
A very basic introduction is given to the r\^oles of division algebras and the related sphere algebras concerning the structure of space-time in the dimensionalities $D\is 3,4,6$ and $10$, with special emphasis on twistors transformations…
A systematic framework for jet definition is developed from first principles of physical measurement, quantum field theory, and QCD. A jet definition is found which: is theoretically optimal in regard of both minimization of detector errors…
We study the differential properties of generalized arc schemes, and geometric versions of Kolchin's Irreducibility Theorem over arbitrary base fields. As an intermediate step, we prove an approximation result for arcs by algebraic curves.