Related papers: Arithmetic trialitarian hyperbolic lattices are no…

In "Non arithmetic super rigid groups: counter examples to Platonov's conjecture" Bass and Lubotzky gave a counter example to Platonov's conjecture by presenting an example of a linear group with super-rigidity which is not an arithmetic…

Let X be an affine variety and L be a solvable Lie subalgebra of Lie(Aut(X)) generated by a finite collection of locally finite Lie subalgebras. The authors of [arXiv:2507.09679] wondered whether L is itself locally finite. Here we present…

In this paper, we give a complete characterization on which finitely generated subgroups of finitely generated $3$-manifold groups are separable. Our characterization generalizes Liu's spirality character on $\pi_1$-injective immersed…

We show that all the currently known non-arithmetic lattices in ${\rm PU}(2,1)$ are monodromy groups of higher hypergeometric functions.

We give necessary conditions for certain real analytic tube generic submanifolds in C^n to be locally algebraizable. As an application, we exhibit families of real analytic non locally algebraizable tube generic submanifolds in C^n. During…

We prove that there exist finitely generated, stably finite algebras which are non linear sofic. This was left open by Arzhantseva and P\u{a}unescu in 2017.

We prove that every local derivation on a finite-dimensional semisimple Lie algebra over an algebraically closed field of characteristic zero is a derivation. We also give examples of finite-dimensional nilpotent Lie algebras $\mathcal{L}$…

We prove that the semistability growth of hyperbolic groups is linear, which implies that hyperbolic groups which are sci (simply connected at infinity) have linear sci growth. Based on the linearity of the end-depth of finitely presented…

Let $L$ be a line bundle on a scheme $X$, proper over a field. The property of $L$ being nef can sometimes be "thickened", allowing reductions to positive characteristic. We call such line bundles arithmetically nef. It is known that a line…

We study gradings by noncommutative groups on finite dimensional Lie algebras over an algebraically closed field of characteristic zero. It is shown that if $L$ is gradeg by a non-abelian finite group $G$ then the solvable radical $R$ of…

We give a Super-Rigidity theorem a la Margulis which applies for a wider class of groups. In particular it applies to subgroups which are not assumed to be lattices in the ambient group. Our proof is based on the notion of Algebraic…

Complex hyperbolic triangle groups were first considered by Mostow in building the first nonarithmetic lattices in PU(2, 1). They are a natural generalization of the classical triangle groups acting on the hyperbolic plane. A well-known…

The principle result of this article is the determination of the possible finite subgroups of arithmetic lattices in U(2,1).

We prove that triangle Artin groups of the type $A_{2,3,2n}$ are residually finite for all $n\geq4$. This requires splitting these triangle Artin groups as graphs of groups and then proving that each of these graphs of groups has finite…

We prove that acylindrically hyperbolic groups are monotileable. That is, every finite subset of the group is contained in a finite tile. This provides many new examples of monotileable groups, and progress on the question of whether every…

The toric Hilbert scheme of a lattice L in Z^n is the multigraded Hilbert scheme parameterizing all ideals in k[x_1,...,x_n] with Hilbert function value one for every degree in the grading monoid N^n/L. In this paper we show that if L is…

We prove that a regular elliptic isometry $f$ of complex hyperbolic space $\mathbf{H}_{\mathbb{C}}^2$ preserves a Lagrangian plane through its fixed point as a non-involution if and only if $f$ is real elliptic. In this case, the isometry…

We give a description of definable sets $P=(p_1,..., p_m)$ in a free non-abelian group $F$ and in a torsion-free non-elementary hyperbolic group $G$ that follows from our work on the Tarski problems. This answers Malcev's question for $F$.…

We study locally finite varieties (=primitive classes) of linear algebras over finite fields. We do not assume that our algebras are associative or Lie. We are interested in the basic properties of finite algebras in these varieties such…

We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type $D_n$ and those of exceptional type and rank…