Related papers: Non-arithmetic monodromy of higher hypergeometric …

In this paper we produce many examples of thin subgroups of special linear groups that are isomorphic to the fundamental groups of non-arithmetic hyperbolic manifolds. Specifically, we show that the non-arithmetic lattices in…

We present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-)acylindrically on finite products of $\delta$-hyperbolic spaces with general type factors and associated subdirect products.…

We establish an arithmeticity vs. non-linearity alternative for irreducible lattices in suitable product groups, such as for instance products of topologically simple groups. This applies notably to a (large class of) Kac-Moody groups. The…

A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in $\mathbf{PSO}_{7,1}(\mathbb{R})$ are not LERF. This result, together with…

We show that S-arithmetic lattices in semisimple Lie groups with no rank one factors are quasi-isometrically rigid.

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…

Deligne and Mostow constructed a class of lattices in PU(2,1) using monodromy of hypergeometric functions. Later, Thurston reinterpreted them in terms of cone metrics on the sphere. In this spirit we construct a fundamental domain for all…

We establish character rigidity for all non-uniform higher-rank irreducible lattices in semisimple groups of characteristic other than 2. This implies stabilizer rigidity for probability measure preserving actions and rigidity of invariant…

Let $\Gamma$ be a lattice in $\mathrm{SO}_0(n, 1)$. We prove that if the associated locally symmetric space contains infinitely many maximal totally geodesic subspaces of dimension at least $2$, then $\Gamma$ is arithmetic. This answers a…

We show that the fundamental groups of all non-compact, arithmetic, hyperbolic, $n$-manifolds for $n\geq 4$ contain thin surface subgroups. As a consequence of the proof of this theorem we also show that the fundamental groups of the…

We show that the isometry group of a finite-volume hyperbolic 3-manifold acts simply transitively on many of its closed geodesics. Combining this observation with the Virtual Special Theorems of the first author and Wise, we show that every…

We classify non symplectic prime order automorphisms and all finite order symplectic automorphism groups of generalised Kummer fourfolds using lattice theory and recent results on ample cones and monodromy groups. We study various geometric…

In this work, we examine one two-parameter family of sets consisting of functions holomorphic in the unit disk, previously investigated by several mathematicians. We focus on the set-theoretic properties of this family, identify the general…

We obtain infinitely many (non-conjugate) representations of 3-manifold fundamental groups into a lattice in the holomorphic isometry group of complex hyperbolic space. The lattice is an orbifold fundamental group of a branched covering of…

Let G be a lattice in PSL(2,C). The pro-normal topology on G is defined by taking all cosets of non-trivial normal subgroups as a basis. This topology is finer than the pro-finite topology, but it is not discrete. We prove that every…

We obtain an infinite family of orthogonal hypergeometric groups, which are higher rank arithmetic groups. We also list cases of arithmetic hypergeometric groups whose real Zariski closure is O(2,3).

We show that for a typical high rank arithmetic lattice $\Gamma$, there exist finite index subgroups $\Gamma_{1}$ and $\Gamma_{2}$ such that $\Gamma_{1} \not\simeq \Gamma_{2}$ while $\widehat{\Gamma_{1}} \simeq \widehat{\Gamma_{2}}$. But…

We explore the thinness of hypergeometric groups of type $\mathrm{Sp}(4)$ and $\mathrm{Sp}(6)$ by applying a new approach of computer-assisted ping pong. We prove the thinness of $17$ hypergeometric groups with maximally unipotent monodromy…

Finite hypergeometric functions are complex valued functions on finite fields which are the analogue of the classical analytic hypergeometric functions. From the work of N.M.Katz it follows that their values are traces of Frobenius on…

Similar to the symplectic cases, there is a family of fourteen orthogonal hypergeometric groups with a maximally unipotent monodromy (cf. Table 1.1). We show that two of the fourteen orthogonal hypergeometric groups associated to the pairs…