相关论文: Differential-algebraic jet spaces preserve interna…

Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite…

We introduce the Frenet theory of curves in dual space $\d^3$. After defining the curvature and the torsion of a curve, we classify all curves in dual plane with constant curvature. We also establish the fundamental theorem of existence in…

We study the properties of orthogonality to the constants and disintegration for autonomous algebraic differential equations. We present a criterion of orthogonality to the constants for absolutely irreducible real $D$-varieties relying on…

We give a self-contained presentation of the basic results on jet schemes of singular varieties. Applications are given to invariants of singularities, such as minimal log discrepancies. We simplify our older approach to Inversion of…

Fractons and other subdimensional particles are an exotic class of emergent quasi-particle excitations with severely restricted mobility. A wide class of models featuring these quasi-particles have a natural description in the language of…

Swarm and constellation reconfiguration can be viewed as motion of an unordered point configuration in an ambient space. Here, we provide persistence-stable, symmetry-invariant geometric representations for comparing and monitoring…

The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…

In this paper we carry out analysis and geometry for a class of infinite dimensional manifolds, namely, compound configuration spaces as a natural generalization of the work \cite{AKR97}. More precisely a differential geometry is…

For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to…

Interaction models describe distributed systems as algebraic terms, with gates marking interaction points between local views. Composing local models into a coherent global one requires aligning these gates while respecting the algebraic…

We present herewith certain thoughts on the important subject of nowadays physics, pertaining to the so-called ``singularities'', that emanated from looking at the theme in terms of ADG (: abstract differential geometry). Thus, according to…

We isolate a geometric mechanism that complements the dynamical suppression of macroscopic interference: In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of…

We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite…

We consider the discretization and subsequent model reduction of a system of partial differential-algebraic equations describing the propagation of pressure waves in a pipeline network. Important properties like conservation of mass,…

The principles of a previously developed formalism for the covariant treatment of multi-scalar fields for which (as in a nonlinear sigma model) the relevant target space is not of affine type -- but curved -- are recapitulated. Their…

In this talk the description of gauge theories associated with internal symmetries is extended to the case in which the symmetry group is the space-time translation group (recovering Einstein's theory) using the standard jet-bundle…

There is an interesting dichotomy between a space-time metric considered as external field in a flat background and the same considered as an intrinsic part of the geometry of space-time. We shall describe and compare two other external…

Jets frames, that is a generalisation of ordinary frames on a manifold, are described in a language similar to that of gauge theory. This is achieved by constructing the Cartan geometry of a manifold with respect to the diffeomorphism…

In this second part of the paper, dedicated to theories with extra dimensions, a new physical notion about the "tensor length scale" is introduced, based on the gravitational theories with covariant and contravariant metric tensor…

Coherent structures play an important role in the near-field of shear flows such as round jets. In the following the near-field of a round jet is numerically investigated , this for different initial conditions. Two configurations are…