Related papers: An algebraic geometry question and wave turbulence
Intermittency is an essential property of astrophysical fluids, which demonstrate an extended inertial range. As intermittency violates self-similarity of motions, it gets impossible to naively extrapolate the properties of fluid obtained…
This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with…
We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and…
Inhomogeneous media commonly support a discrete number of wave modes that are trapped along interfaces defined by spatially varying parameters. When they are robust against continuous deformations of parameters, such waves are said to be of…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
This paper explores the sheaves with the action of a lie algebra and computes their cohomology in a new category. Then in the following sections, We try to generalize a classical result in [GM, Ch. IV] about exterior algebra. We add the…
We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized…
We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized…
We present an introductory overview of several challenging problems in the statistical characterisation of turbulence. We provide examples from fluid turbulence in three and two dimensions, from the turbulent advection of passive scalars,…
In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold $\mathbb{L}$, there exists a global trivialization of the tangent bundle, which defines a map…
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large…
The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also…
Gyrokinetics is a rich and rewarding playground to study some of the mysteries of modern physics. In this thesis I present work, motivated by the quest for fusion energy, which seeks to uncover some of the inner workings of turbulence in…
The relation between algebraic and traditional calculations of molecular vibrations is investigated. An explicit connection between interactions in configuration space and the corresponding algebraic interactions is established.
We will pursue a way of building up an algebraic structure that involves, in a mathematical abstract way, the well known Grassmann variables. The problem arises when we tried to understand the grassmannian polynomial expansion on the scope…
This work introduces a geometrical method for analyzing transient gravitational waves recorded at interferometric observatories. This approach is intended to aid in assessing the performance and sensitivity of next-generation detector…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
Duality of curves is one of the important aspects of the ``classical'' algebraic geometry. In this paper, using this foundation, the duality of tropical polynomials is constructed to introduce the duality of Non-Archimedean curves. Using…
One of the questions investigated in deformation theory is to determine to which algebras can a given associative algebra be deformed. In this paper we investigate a different but related question, namely: for a given associative…