Related papers: Genericity, the Arzhantseva-Ol'shanskii method and…

It is shown that the problem of reduction can be formulated in a uniform way using the theory of invariants. This provides a powerful tool of analysis and it opens the road to new applications of these algebras, beyond the context of…

The paper follows two interconnected directions. 1. Let $G$ be a Roelcke precompact closed subgroup of the group $\Sym(\omega)$ of permutations of the natural numbers. Then $\Inn(G)$ is closed in $\Aut(G)$, where $\Aut(G)$ carries the…

We generalise Merzlyakov's theorem about the first-order theory of non-abelian free groups to all acylindrically hyperbolic groups. As a corollary, we deduce that if $G$ is an acylindrically hyperbolic group and $E(G)$ denotes the unique…

We introduce and investigate different definitions of effective amenability, in terms of computability of F{\o}lner sets, Reiter functions, and F{\o}lner functions. As a consequence, we prove that recursively presented amenable groups have…

This work is devoted to the relativistic generalization of Chasles' theorem, namely to the proof that every proper orthochronous isometry of Minkowski spacetime, which sends some point to its chronological future, is generated through the…

We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…

The Baumslag group had been a candidate for a group with an extremely difficult word problem until Myasnikov, Ushakov, and Won succeeded to show that its word problem can be solved in polynomial time. Their result used the newly developed…

A subgroup $H$ of a group $G$ is $commensurated$ in $G$ if for each $g\in G$, $gHg^{-1}\cap H$ has finite index in both $H$ and $gHg^{-1}$. If there is a sequence of subgroups $H=Q_0\prec Q_1\prec ...\prec Q_{k}\prec Q_{k+1}=G$ where $Q_i$…

In this paper the whole geometrical set-up giving a conformally invariant holographic projection of a diffeomorphism invariant bulk theory is clarified. By studying the renormalization group flow along null geodesic congruences a…

We study the complexity of counting (weighted) planar graph homomorphism problem $\tt{Pl\text{-}GH}(M)$ parametrized by an arbitrary symmetric non-negative real valued matrix $M$. For matrices with pairwise distinct diagonal values, we…

Two graphs $G$ and $H$ are homomorphism indistinguishable over a graph class $\mathcal{F}$ if they admit the same number of homomorphisms from every graph $F \in \mathcal{F}$. Many graph isomorphism relaxations such as (quantum) isomorphism…

We study the cohomology $H^*_{\lambda \omega}(G/\Gamma, {\mathbb C})$ of the deRham complex $\Lambda^*(G/\Gamma)\otimes{\mathbb C}$ of a compact solvmanifold $G/\Gamma$ with a deformed differential $d_{\lambda \omega}=d + \lambda\omega$,…

We study the existence of homomorphisms between Out(F_n) and Out(F_m) for n > 5 and m < n(n-1)/2, and conclude that if m is not equal to n then each such homomorphism factors through the finite group of order 2. In particular this provides…

In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…

We consider a generalization of finding a homomorphism from an input digraph $G$ to a fixed digraph $H$, HOM($H$). In this setting, we are given an input digraph $G$ together with a list function from $G$ to $2^H$. The goal is to find a…

Fix a finite group $G$. We study the computational complexity of counting problems of the following flavor: given a group $\Gamma$, count the number of homomorphisms $\Gamma \to G$. Our first result establishes that this problem is…

A fundamental result in the study of graph homomorphisms is Lov\'asz's theorem that two graphs are isomorphic if and only if they admit the same number of homomorphisms from every graph. A line of work extending Lov\'asz's result to more…

We show that many normal subgroups of the braid group modulo its centre, and of the mapping class group of a sphere with marked points, have the property that their automorphism and abstract commensurator groups are mapping class groups of…

We provide a new foundational approach to the generalization of terms up to equational theories. We interpret generalization problems in a universal-algebraic setting making a key use of projective and exact algebras in the variety…

We prove that for torsion-free amenable ample groupoids, an isomorphism in groupoid homology induced by an \'etale correspondence yields an isomorphism in the K-theory of the associated $\mathrm{C}^\ast$-algebras. We apply this to extend X.…