Related papers: Discrete group actions on Stein domains in complex…

This work investigates analytic Hilbert modules $\mathcal{H}$, over the polynomial ring, consisting of holomorphic functions on a $G$-space $\Omega \subset \mathbb{C}^m$ that are homogeneous under the natural action of the group $G$. In a…

We show that real semi-simple Lie groups of higher rank contain (infinitely generated) discrete subgroups with full limit sets in the corresponding Furstenberg boundaries. Additionally, we provide criteria under which discrete subgroups of…

We give a proof, based on thermodynamic formalism, of a theorem in bounded cohomology extending a foundational result of Burger and Monod: if $\Gamma$ is an irreducible uniform lattice in a non-compact connected semisimple Lie group of real…

In these lectures we consider how algebraic properties of discrete subgroups of Lie groups restrict the possible actions of those groups on surfaces. The results show a strong parallel between the possible actions of such a group on the…

Let $G$ be a noncompact semisimple Lie group, $\Gamma$ be an irreducible cocompact lattice in $G$, and $P<G$ be a minimal parabolic subgroup. We consider the dynamics of $P$ acting on $G/\Gamma$ by left translation. For any infinite subset…

We determine all holomorphically separable complex manifolds of dimension $p+q$ which admits a smooth envelope of holomorphy such that the general indefinite unitary group of size $p+q$ acts effectively by holomorphic transformations. Also…

We consider pro-isomorphic zeta functions of the groups $\Gamma(\mathcal{O}_K)$, where $\Gamma$ is a unipotent group scheme defined over $\mathbb{Z}$ and $K$ varies over all number fields. Under certain conditions, we show that these…

Developing ideas of \cite{Fei}, we introduce canonical cosimplicial cohomology of meromorphic functions for infinite-dimensional Lie algebra formal series with prescribed analytic behavior on domains of a complex manifold $M$. Graded…

Let $M$ be a compact, real analytic manifold and $G$ be the Lie group of all real-analytic diffeomorphisms of $M$, which is modelled on the space ${\mathfrak g}$ of real-analytic vector fields on $M$. We study flows of time-dependent…

Let $X=G/H$ be a homogeneous space of a Lie group $G$. When the isotropy subgroup $H$ is non-compact, a discrete subgroup $\Gamma$ may fail to act properly discontinuously on $X$. In this article, we address the following question: in the…

A section of a Riemannian $G$-manifold $M$ is a closed submanifold $\Sigma$ which meets each orbit orthogonally. It is shown that the algebra of $G$-invariant differential forms on $M$ which are horizontal in the sense that they kill every…

Suppose $\Gamma$ is an arithmetic group defined over a global field $K$, that the $K$-type of $\Gamma$ is $A_n$ with $n \geq 2$, and that the ambient semisimple group that contains $\Gamma$ as a lattice has at least two noncocompact…

We consider the moduli space ${\cal M}(G)$ of $G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a semisimple complex Lie group, and study the action of a finite group $\Gamma$ on ${\cal M}(G)$ induced by a holomorphic…

Let $G\subset\GL(\BC^r)$ be a finite complex reflection group. We show that when $G$ is irreducible, apart from the exception $G=\Sgot_6$, as well as for a large class of non-irreducible groups, any automorphism of $G$ is the product of a…

Diffeomorphism groups $G$ of manifolds $M$ on locally $\bf F$-convex spaces over non-Archimedean fields $\bf F$ are investigated. It is shown that their structure has many differences with the diffeomorphism groups of real and complex…

Let $\Gamma$ be a compact Polish group of finite topological dimension. For a countably infinite subset $S\subseteq \Gamma$, a domatic $\aleph_0$-partition (for its Schreier graph on $\Gamma$) is a partial function…

If $V$ is an analytic set in a pseudoconvex domain $\Omega$, we show there is always a pseudoconvex domain $G \subseteq \Omega$ that contains $V$ and has the property that every bounded holomorphic function on $V$ extends to a bounded…

We prove that every reduced Stein space admits a holomorphic function without critical points. Furthermore, any closed discrete subset of such a space is the critical locus of a holomorphic function. We also show that for every complex…

Consider a unitary representation $\pi$ of a discrete group $G$, which, when restricted to an almost normal subgroup $\Gamma\subseteq G$, is of type II. We analyze the associated unitary representation $\overline{\pi}^{\rm{p}}$ of $G$ on…

Let G be a real semisimple Lie group with no compact factors and finite centre, and let $\Lambda$ be a lattice in G. Suppose that there exists a homomorphism from $\Lambda$ to the outer automorphism group of a right-angled Artin group…