Related papers: Solution to an isotopism question concerning rank …
We determine the tensor rank of all semifields of order 16 over $\mathbb{F}_2$ and of all semifields of order 81 over $\mathbb{F}_3$. Our results imply that some semifields of order 81 have lower multiplicative complexity than the finite…
In this article we construct a new family of semifields, containing and extending two well-known families, namely Albert's generalised twisted fields and Petit's cyclic semifields (also known as Johnson-Jha semifields). The construction…
This is the second of a series of papers outlining an approach to the classification of $\mathcal{N}{=}2$ superconformal field theories at rank 2 via a systematic analysis of their Coulomb branches, mathematically described by special…
For each integer \( n \geq 3 \), we construct a self-dual regular 3-polytope \( \mathcal{P} \) of type \( \{n, n\} \) with \( 2^n n \) flags, resolving two foundamental open questions on the existence of regular polytopes with certain…
We classify the rank two commutative semifields which are 8-dimensional over their center $\mathbb{F}_{q}$. This is done using computational methods utilizing the connection to linear sets in $\mathrm{PG}(2,q^{4})$. We then apply our…
In this article, we present two new constructions for semifields of order $p^{2m}$. Together, the constructions unify and generalize around a dozen distinct semifield constructions, including both the oldest known construction by Dickson…
Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type of the semifield generated by the two neutral elements. For…
The present work investigates regular, semiregular, and chiral polytopes of any rank $d\geq 3$, whose automorphism groups are 2-groups. There is a large variety of rather small finite regular or alternating semiregular polytopes with…
We study the four-dimensional N=2 superconformal field theories that describe D3-branes probing the recently constructed N=2 S-folds in F-theory. We introduce a novel, infinite class of superconformal field theories related to S-fold…
We introduce a new class of possibly noncompact n-dimensional manifolds without boundary associated to finite data which we call topological automata. This class is large enough to contain many interesting examples of open 2-dimensional and…
For each $d\geq 3$, $n \geq 10$, and $k_1, k_2, \ldots, k_{d-1}\geq 2$ with $k_1+k_2+\ldots+k_{d-1}\leq n-1$, we construct a regular $d$-polytope whose automorphism group is of order $2^n$ and whose Schl\"afli type is $\{2^{k_1},2^{k_2},…
Nurowski showed that any generic 2-plane field $D$ on a 5-manifold $M$ determines a natural conformal structure $c_D$ on $M$; these conformal structures are exactly those (on oriented $M$) whose normal conformal holonomy is contained in the…
The aim of this paper is twofold. The first part is concerned with the associated and the so-called co-polynomials, i.e. new sequences obtained when finite perturbations of the recurrence coefficients are considered. In the second part we…
We study mass deformations of N=2 superconformal field theories with ADE global symmetries on a D3-brane. The N=2 Seiberg-Witten curves with ADE symmetries are determined by the Type IIB 7-brane backgrounds which are probed by a D3-brane.…
We introduce a series of $\Z_2^n$-graded quasialgebras $\bbP_n(m)$ which generalizes Clifford algebras, higher octonions, and higher Cayley algebras. The constructed series of algebras and their minor perturbations are applied to contribute…
In this paper we introduce a model theoretic construction for the theories of uniform layered domains and semifields introduced in the paper of Izhakian, Knebusch and Rowen. We prove that, for a given layering semiring L, the theory of…
The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds is a notoriously difficult problem. Isomorphism classes of such vector bundles are not uniquely determined by their Chern classes, in contrast to the…
We construct infinite new classes of $AdS_4\times S^1\times S^5$ solutions of type IIB string theory which have non-trivial $SL(2,\mathbb{Z})$ monodromy along the $S^1$ direction. The solutions are supersymmetric and holographically dual,…
In a companion paper [On semiclassical orthogonal polynomials via polynomial mappings, J. Math. Anal. Appl. (2017)] we proved that the semiclassical class of orthogonal polynomials is stable under polynomial transformations. In this work we…
Let $F_{q}$ be a finite field of cardinality $q$. A polynomial over finite field $F_{q}$ of the form $\sum_{i,j}a_{ij}x^{p^{i}+p^{j}}$ is called a Dembowski-Ostrom (DO) polynomial. The Dembowski-Ostrom conjecture says that a planar…