Related papers: Geometric aspects of higher order variational prin…
Jets of mappings introduced by Ehresmann are still the most useful objects for formulating geometric frameworks of physical theories. We are proposing modifications designed to make jet theory less dependent on local coordinates. Extensions…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
The differential geometric aspects of Geometric Phases are reviewed.
Recent theoretical developments in the description of jet evolution in the quark gluon plasma have allowed to account for the effects of hydrodynamic gradients in the medium modified jet spectra. These constitute a crucial step towards…
We show how the theory of $\mathbb{Z}_2^n$ -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such…
In this paper, we collect the fundamental basic properties of jet modules in algebraic geometry and related properties of differential operators. We claim no originality but we want to provide a reference work for own research and the…
We introduce a novel jet substructure method which exploits the variation of observables with respect to a sampling of phase-space boundaries quantified by the variability. We apply this technique to identify boosted W boson and top quark…
Relativistic mechanics on an arbitrary manifold is formulated in the terms of jets of its one-dimensional submanifolds. A generic relativistic Lagrangian is constructed. Relativistic mechanics on a pseudo-Riemannian manifold is particularly…
Some topics in the theory of jets are reviewed. These include jet precession, unconfined jets, the origin of knots, the internal shock model as a unifying theme from protostellar jets to Gamma-ray bursts, relations between the…
Conformal geodesics are solutions to a system of third order of equations, which makes a Lagrangian formulation problematic. We show how enlarging the class of allowed variations leads to a variational formulation for this system with a…
Jet substructure observables are crucial for exploring the effects of the hot, dense medium and differentiating between quark and gluon jets. In this paper, we investigate the modification of jet shape by calculating the differential girth…
This paper belongs to the realm of conformal geometry and deals with Euclidean submanifolds that admit smooth variations that are infinitesimally conformal. Conformal variations of Euclidean submanifolds is a classical subject in…
Latent representations are an important theme in modern machine learning. Any network training with the notion of locality introduces a latent geometry which we can analyze with the help of differential geometry, specifically information…
In the first talk I discuss the usefulness of jet grooming for testing jet quenching mechanisms, and I present a calculation of soft-drop jet mass distribution in proton-proton and heavy ion collisions. In the second talk I discuss the…
This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…
This article studies jet schemes of monomial schemes. They are known to be equidimensional but usually are not reduced. We thus investigate their structure further, giving a formula for the multiplicity along every component of the jet…
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
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 discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first-order…
A brief overview of jets and their central drivers is presented, with a focus on accreting black hole systems. In particular, scaling relations that elucidate some basic properties of the engines are derived, and the implications for the…