Related papers: Fra\"iss\'e structures and a conjecture of Fursten…

A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…

Let $k$ be an algebraically closed field of positive characteristic, $G$ a reductive group over $k$, and $V$ a finite dimensional $G$-module. Let $B$ be a Borel subgroup of $G$, and $U$ its unipotent radical. We prove that if $S=\Sym V$ has…

We analyze constraints for embedding local SU(5) F-theory GUTs into consistent compactifications and construct explicit three-generation models based on the geometry of arXiv:0904.3932. The key tool for studying constraints in this problem…

Let $\mathfrak g$ be a finite-dimensional Lie algebra. The symmetric algebra $\mathcal S(\mathfrak g)$ is equipped with the standard Lie-Poisson bracket. In this paper, we elaborate on a surprising observation that one naturally associates…

We define for a topological group G and a family of subgroups F two versions for the classifying space for the family F, the G-CW-version E_F(G) and the numerable G-space version J_F(G). They agree if G is discrete, or if G is a Lie group…

Let G be a complex semisimple Lie group, K a maximal compact subgroup and V an irreducible representation of K. Denote by M the unique closed orbit of G in P(V) and by O its image via the moment map. For any measure on M we construct a map…

We investigate some of the effects of the lack of compactness in the critical Folland-Stein-Sobolev embedding in very general (possible non-smooth) domains, by proving via De Giorgi's $\Gamma$-convergence techniques that optimal functions…

In a 2004 article, Udo Baumgartner and George Willis used ideas from the structure theory of totally disconnected, locally compact groups to achieve a better understanding of the contraction group U_f associated with an automorphism f of…

We devise a fairly general sufficient condition ensuring that the endomorphism monoid of a countably infinite ultrahomogeneous structure (i.e. a Fra\"{\i}ss\'{e} limit) embeds all countable semigroups. This approach provides us not only…

We study topologization of the semigroup $\mathscr{O\!\!I}\!_n(L)$ of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set $(L,\leqslant)$. In particular we show that every $T_1$ left-topological…

We describe the structure of finite groups with $\mathfrak{F}$-subnormal or self-normalizing primary cyclic subgroups when $\mathfrak{F}$ is a subgroup-closed saturate superradical formation containing all nilpotent groups. We prove that…

Last years a number of papers were devoted to describing automorphisms of semigroups of endomorphisms of free finitely generated universal algebras of some varieties: groups, semigroups, associative commutative algebras, inverse semigroups,…

We try to build, provably in ZFC, for a first order T a model in which any isomorphism between two Boolean algebras is definable. The problem, compared to [Sh:384], is with pseudo-finite Boolean algebras. A side benefit is that we do not…

Let $M$ be a Fra\"{i}ss\'{e} structure (a countably infinite ultrahomogeneous structure). We refer to the class of structures embeddable in $M$ as the $\omega$-age of $M$. We consider the following two properties of $M$: we say that $M$ has…

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 construct in ZFC a countably compact group without non-trivial convergent sequences of size $2^{\mathfrak{c}}$, answering a question of Bellini, Rodrigues and Tomita. We also construct in ZFC a selectively pseudocompact group which is…

We discuss the Bohr compactification of a pseudofinite group, motivated by a question of Boris Zilber. Basically referring to results in the literature we point out (i) the Bohr compactification of an ultraproduct of finite simple groups is…

Roelcke non-precompactness, non-simplicity, and non-amenability of the automorphism group of the Fra\"iss\'e limit of finite Heyting algebras are examined among others.

Given a semigroup $G$ and a bounded function $f: G \to \mathbb{C}$, a topological Furstenberg system of $f$ is a topological dynamical system $\mathbb{X}=(X, (T_g)_{g \in G})$ that encodes the dynamical behaviour of $f$. We show that…

In this paper we investigate the connections between Ramsey properties of Fraisse classes K and the universal minimal flow M(G_K) of the automorphism group G_K of their Fraisse limits. As an extension of a result of Kechris, Pestov and…