Related papers: Lattice Models of Finite Fields
We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…
In this paper, we consider the direct and inverse problems of the description of lattice positive random fields by various systems of finite-dimensional (as well as one-point) probability distributions parameterized by boundary conditions.…
Logarithmic Conformal Field Theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self avoiding walks, etc.), or of critical points in several classes of disordered systems…
We establish a connection between finite fields and finite dynamical systems. We show how this connection can be used to shed light on some problems in finite dynamical systems and in particular, in linear systems.
In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…
The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.
We develop the theory of mixed finite elements in terms of special inverse systems of complexes of differential forms, defined over cellular complexes. Inclusion of cells corresponds to pullback of forms. The theory covers for instance…
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
In this paper, we study several topics on additive decompositions of primitive elemements in finite fields. Also we refine some bounds obtained by Dartyge and S\'{a}rk\"{o}zy and Shparlinski.
Lattice field theory methods, usually associated with non-perturbative studies of quantum chromodynamics, are becoming increasingly common in the calculation of ground-state and thermal properties of strongly interacting non-relativistic…
We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings. We introduce a method of presenting a transformation between…
On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the…
One of the traditional applications of relation algebras is to provide a setting for infinite-domain constraint satisfaction problems. Complexity classification for these computational problems has been one of the major open research…
I give a review of existing frameworks, which are designed to analyse lattice data in the three-particle sector. A particular emphasis is laid on the foundations of the theory, where the separation of the short- and long-range effects plays…
We investigate the structure and representation theory of finite-dimensional $\mathbb{Z}$-graded Lie algebras, including the corresponding root systems and Verma, irreducible, and Harish-Chandra modules. This extends the familiar theory for…
In algebraic number theory, the finiteness of the Picard group of an order in a number field is generally proved via a lattice argument: the order forms a lattice and every ideal class contains an integral ideal with a small enough non-zero…
This article is the first of an intended series of works on the model theory of Ultrafinitism. It is roughly divided into two parts. The first one addresses some of the issues related to ultrafinitistic programs, as well as some of the core…
We use the complex $\phi^4$ field at finite density as a model system for developing further techniques based on worldline formulations of lattice field theories. More specifically we: 1) Discuss new variants of the worm algorithm for…
The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…
An alternative approach to lattice gauge theory has been under development for the past decade. It is based on discretizing the operator Heisenberg equations of motion in such a way as to preserve the canonical commutation relations at each…