Related papers: Quantitative Density under Higher Rank Abelian Alg…

For actions with a dense orbit of a connected noncompact simple Lie group $G$, we obtain some global rigidity results when the actions preserve certain geometric structures. In particular, we prove that for a $G$-action to be equivalent to…

Let $K$ be a number field with ring of integers $\mathcal O$. After introducing a suitable notion of density for subsets of $\mathcal O$, generalizing that of natural density for subsets of $\mathbb Z$, we show that the density of the set…

Let $\G$ be a group of type rotating automorphisms of an affine building $\cB$ of type $\wt A_2$. If $\G$ acts freely on the vertices of $\cB$ with finitely many orbits, and if $\Omega$ is the (maximal) boundary of $\cB$, then…

Let $\mathbb{K}$ be an algebraically closed field of characteristic zero and $\mathbb{G}_a$ be the additive group of $\mathbb{K}$. We say that an irreducible algebraic variety $X$ of dimension $n$ over the field $\mathbb{K}$ admits an…

The subject of this thesis is the modular group of automorphisms acting on the massive algebra of local observables having their support in bounded open subsets of Minkowski space. After a compact introduction to micro-local analysis and…

Let g be a complex simple Lie algebra and Uq(Lg) its quantum loop algebra, where q is not a root of unity. We give an explicit formula for the quantum Weyl group action of the coroot lattice Q of g on finite-dimensional representations of…

Consider a locally compact group $G=Q\ltimes V$ such that $V$ is abelian and the action of $Q$ on the dual abelian group $\hat V$ has a free orbit of full measure. We show that such a group $G$ can be quantized in three equivalent ways: (1)…

The automorphism group $Aut(X,\mu)$ of a compact, complete metric space $X$ with a Radon measure $\mu$ is a subgroup of $\mathcal{U}(L^2(X,\mu))$-the unitary group of operators on $L^2(X,\mu)$. The $Aut(X,\mu)$-action on the generalized…

Let G be a sofic group and X a compact group that G acts on by automorphisms. Using (and reformulating) the notion of doubly-quenched convergence developed by Austin, we show that in many cases the topological and the measure-theoretic…

Mimicking a recent article of Stefaan Vaes, in which was proved that every locally compact quantum group can act outerly, we prove that we get the same result for measured quantum groupoids, with an appropriate definition of outer actions…

We prove that every smooth action of Z^k, k>1, on the (k+1)-dimensional torus homotopic to an action by hyperbolic linear maps preserves an absolutely continuous measure. This is a first known result concerning abelian groups of…

We study Property (T) for locally compact quantum groups, providing several new characterisations, especially related to operator algebraic ergodic theory. Quantum Property (T) is described in terms of the existence of various Kazhdan type…

We prove a quantum version of the localization formula of Witten that relates invariants of a git quotient with the equivariant invariants of the action. Using the formula we prove a quantum version of an abelianization formula of S. Martin…

Based on the realization of quantum Borcherds-Bozec algebra $\widetilde{\mathbf{U}}$ and quantum generalized Kac-Moody algebra ${}^B\widetilde{\mathbf{U}}$ via semi-derived Ringel-Hall algebra of a quiver with loops, we deduce the braid…

The QED effective action at finite temperature and density is calculated to all orders in an external homogeneous and time-independent magnetic field in the weak coupling limit. The free energy, obtained explicitly, exhibit the expected de\…

We relate Fuglede-Kadison determinants to entropy of algebraic actions of sofic groups in essentially complete generality. This generalizes recent results of Hanfeng Li and Andreas Thom from the amenable case to the sofic case, as well as…

We show that the maximal orbit dimension of a simultaneous Lie group action on n copies of a manifold does not pseudo-stabilize when n increases. We also show that if a Lie group action is (locally) effective on subsets of a manifold, then…

We develop a method for providing quantitative estimates for higher order correlations of group actions. In particular, we establish effective mixing of all orders for actions of semisimple Lie groups as well as semisimple $S$-algebraic…

We prove a decomposition result for a group $G$ acting strongly transitively on the Tits boundary of a Euclidean building. As an application we provide a local to global result for discrete Euclidean buildings, which generalizes results in…

An additive action on an algebraic variety is an effective action of the vector group with an open orbit. We describe projective surfaces with du Val singularities that admit an additive action with a finite number of orbits. In particular,…