Related papers: Pariah moonshine
For each element of the Fischer-Griess Monster sporadic simple group, we construct an infinite dimensional Lie algebra equipped with a projective action of the centralizer of that element. Our construction is given by a string-theoretic…
We study the Diophantine problem (decidability of finite systems of equations) in different classes of finitely generated solvable groups (nilpotent, polycyclic, metabelian, free solvable, etc), which satisfy some natural…
Our main result is that many triangles of Baumslag-Solitar groups collapse to finite groups, generalizing a famous example of Hirsch. A triangle of Baumslag-Solitar groups means a group with three generators, cyclically ordered, with each…
We announce two breakthrough results concerning important questions in the Theory of Computational Complexity. In this expository paper, a systematic and comprehensive geometric characterization of the Subset Sum Problem is presented. We…
We compare the moonshine observation of Eguchi, Ooguri and Tachikawa relating the Mathieu group M_24 and the complex elliptic genus of a K3 surface with the symmetries of geometric structures on K3 surfaces. Two main results are that the…
This paper is a study of the Lie groups of point symmetries admitted by a system describing a non-stationary planar flow of an ideal plastic material. For several types of forces involved in the system, the infinitesimal generators which…
Given a matroid or flag of matroids we introduce several broad classes of polynomials satisfying Deletion-Contraction identities, and study their singularities. There are three main families of polynomials captured by our approach:…
We study the Fraisse limit of the class of all finite simplicial complexes. Whilst the natural model-theoretic setting for this class uses an infinite language, a range of results associated with Fraisse limits of structures for finite…
It is demonstrated that iterative repeating of some simple geometric construction leads unavoidably in the limit to the golden ratio. The procedure appears to be quickly convergent regardless of a ratio of initial elements sizes. This could…
The present survey aims at being a list of Conjectures and Problems in an area of model-theoretic algebra wide open for research, not a list of known results. To keep the text compact, it focuses on structures of finite Morley rank,…
Testing isomorphism of infinite groups is a classical topic, but from the complexity theory viewpoint, few results are known. S{\'e}nizergues and the fifth author (ICALP2018) proved that the isomorphism problem for virtually free groups is…
We give an almost entirely model-theoretic account of both Ramsey classes of finite structures and of generalized indiscernibles as studied in special cases in (for example) [7], [9]. We understand "theories of indiscernibles" to be special…
We consider p-divisible groups (also called Barsotti-Tate groups) in characteristic p, their deformations, and we draw some conclusions. For such a group we can define its Newton polygon (abbreviated NP). This is invariant under isogeny.…
We give several new positive finite presentations for the pure braid group that are easy to remember and simple in form. All of our presentations involve a metric on the punctured disc so that the punctures are arranged "convexly", which is…
Let $P = (\{1,2,\ldots,n,\leq)$ be a poset that is an union of disjoint chains of the same length and $V=\mathbb{F}_q^N$ be the space of $N$-tuples over the finite field $\mathbb{F}_q$. Let $V_i = \mathbb{F}_q^{k_i}$, $1 \leq i \leq n$, be…
The main aim of this article is to study the quantitative structure of projective symplectic groups $PSp_{4}(q)$ with $q>2$ even. Indeed, we prove that the groups $PSp_{4}(q)$ with $q>2$ even are uniquely determined by their orders and the…
We investigate the representations of the symmetry groups of infinite crystals. Crystal symmetries are usually described as the finite symmetry group of a finite crystal with periodic boundary conditions, for which the Brillouin zone is a…
Axial algebras of Monster type are a class of commutative algebras generated by special idempotents called axes. Some motivating examples of these algebras are the Griess algebra and the Norton-Sakuma algebras, relating to the Monster…
In the course of studies of the measure of chaos for the distribution of the prime numbers among the positive integers N arched structures have been found. It is given a brief description of the fine structure of the positive integers…
The E. Cartan's equations defining "simple" spinors (renamed "pure" by C. Chevalley) are interpreted as equations of motions for fermion multiplets in momentum spaces which, in a constructive approach based bilinearly on those spinors,…