Related papers: Simplices and Regular Polygonal Tori in Euclidean …
Ramsey's theorem states that each coloring has an infinite homogeneous set, but these sets can be arbitrarily spread out. Paul Erdos and Fred Galvin proved that for each coloring f, there is an infinite set that is "packed together" which…
Recently, Solecki introduced the notion of Ramsey monoid to produce a common generalization to theorems such as Hindman's theorem, Carlson's theorem, and Gowers' FIN$_k$ theorem. He proved that an entire class of finite monoids is Ramsey.…
We prove an infinite Ramsey theorem for noncommutative graphs realized as unital self-adjoint subspaces of linear operators acting on an infinite dimensional Hilbert space. Specifically, we prove that if V is such a subspace, then provided…
We prove that curve complexes of surfaces are finitely rigid: for every orientable surface S of finite topological type, we identify a finite subcomplex X of the curve complex C(S) such that every locally injective simplicial map from X…
We show that every finitely generated residually finite torsion group $G$ embeds in a finitely generated torsion group $\Gamma$ that is residually finite simple. In particular we show the existence of finitely generated infinite torsion…
We show that the class of finite rooted binary plane trees is a Ramsey class (with respect to topological embeddings that map leaves to leaves). That is, for all such trees P,H and every natural number k there exists a tree T such that for…
We prove that a set of finite perimeter is indecomposable if and only if it is, up to a choice of suitable representative, connected in the 1-fine topology. This gives a topological characterization of indecomposability which is new even in…
A Hausdorff topological semiring is called simple if every non-zero continuous homomorphism into another Hausdorff topological semiring is injective. Classical work by Anzai and Kaplansky implies that any simple compact ring is finite. We…
A central conjecture in inverse Galois theory, proposed by D\`{e}bes and Deschamps, asserts that every finite split embedding problem over an arbitrary field can be regularly solved. We give an unconditional proof of a consequence of this…
Given two semistable, non potentially isotrivial elliptic surfaces over a curve $C$ defined over a field of characteristic zero or finitely generated over its prime field, we show that any compatible family of effective isometries of the…
Among all affine, flat, finitely presented group schemes, we focus on those that are pure, this includes all groups which are extensions of a finite locally free group by a group with connected fibres. We prove that over an arbitrary base…
An old conjecture of Erd\H{o}s and R\'enyi, proved by Schinzel, predicted a bound for the number of terms of a polynomial $g(x) \in \mathbb{C}[x]$ when its square $g(x)^2$ has a given number of terms. Further conjectures and results arose,…
The simplicial wedge construction on simplicial complexes and simple polytopes has been used by a variety of authors to study toric and related spaces, including non-singular toric varieties, toric manifolds, intersections of quadrics and…
Recent work by Forsg{\aa}rd indicates that not every convex lattice polygon arises as the characteristic polygon of an affine dimer or, equivalently, an admissible oriented line arrangement on the torus in general position. We begin the…
In his previous paper, the author proposed as a problem a purely inseparable analogue of the Abhyankar conjecture for affine curves in positive characteristic and gave a partial answer to it, which includes a complete answer for finite…
We consider the following question, concerning associative algebras R over an algebraically closed field k: When can the space of (equivalence classes of) finite dimensional irreducible representations of R be topologically embedded into a…
We prove that every countable left-ordered group embeds into a finitely generated left-ordered simple group. Moreover, if the first group has a computable left-order, then the simple group also has a computable left-order. We also obtain a…
Invariant torus are constructed under assumption that the homogeneous system admits an exponential dichotomy on the semi-axes. The main result is closely related with the well-known Palmer's lemma and results of Boichuk A.A., Samoilenko…
We show that the \s{\phi}-labeled Thompson groups and the twisted Brin--Thompson groups are boundedly acyclic. This allows us to prove several new embedding results for groups. First, every group of type $F_n$ embeds quasi-isometrically…
A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fra\"iss\'e classes of finite relational structures satisfying the Ramsey property. The…