Related papers: Open Problems in the Theory of Ample Fields
We review main features and problems of higher spin field theory and flash some ways along which it has been developed over last decades.
Galois connections were introduced by Ore and have proved useful in a wide variety of mathematical areas. While Galois connections play on the ground of posets (or more generally of quasiordered sets or qosets), we extend this notion to…
This is a guide to the construction of nonlinear number fields, which includes new points not found in our earlier article ``Geometric Galois theory, nonlinear number fields and a Galois group interpretation of the idele class group''.
Since it first emerged in Wijsman's seminal work [29], the Wijsman topology has been intensively studied in the past 50 years. In particular, topological properties of Wijsman hyperspaces, relationships between the Wijsman topology and…
Let $H$ be a skew field of finite dimension over its center $k$. We solve the Inverse Galois Problem over the field of fractions $H(X)$ of the ring of polynomial functions over $H$ in the variable $X$, if $k$ contains an ample field.
We offer a new perspective on the closed graph theorem and the open mapping theorem for separated barrelled spaces and fully complete spaces.
The problem of constructing curves with many points over finite fields has received considerable attention in the recent years. Using the class field theory approach, we construct new examples of curves ameliorating some of the known…
When p divides the ordering of Galois group, the distribution of the Sylow p-subgroup of Cl(K) is closely related to the problem of counting fields with certain specifications. Moreover, different orderings of number fields affect the…
Finite fields form an important chapter in abstract algebra, and mathematics in general. We aim to provide a geometric and intuitive model for finite fields, involving algebraic numbers, in order to make them accessible and interesting to a…
Effective field theories offer a powerful method to unify diverse models under a small set of control parameters, allowing systematic expansions around well-established theories. These techniques, developed in particle physics, were…
This paper develops from scratch a theory of Galois rings and orders over arbitrary fields. Our approach is different from others in the literature in that there is no non-modularity assumption. We prove, when the field is algebraically…
This is a brief introduction to the subject of Conformal Field Theory on surfaces with boundaries and crosscaps, which describes the perturbative expansion of open string theory.
This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…
We compare several definitions of the Galois group of a linear difference equation that have arisen in algebra, analysis and model theory and show, that these groups are isomorphic over suitable fields. In addition, we study properties of…
Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…
Geometric Hydrodynamics has flourished ever since the celebrated 1966 paper of V. Arnold. In this paper we present a collection of open problems along with several new constructions in fluid dynamics and a concise survey of recent…
Recent work in higher algebra allows the reinterpretation of a classical description of the Eilenberg-MacLane spectrum $H\mathbb{Z}$ as a Thom spectrum, in terms of a kind of derived Galois theory. This essentially expository talk…
We describe relations between maximal subfields in a division ring and in its rational extensions. More precisely, we prove that properties such as being Galois or purely inseparable over the centre generically carry over from one to…
We prove that there are infinitely many finite simple groups of symplectic Lie type, of any specified characteristic and rank, which appear as Galois groups over the field of rational numbers. This generalizes a result of Wiese, which…
We take a tour through the past, present and future of Effective Field Theory, with applications ranging from LHC physics to cosmology.