We present a new simple proof of the fact that certain group manifolds as well as certain homogeneous spaces G/H of dimension 4n admit a quaternionic triple of integrable complex structures that are covariantly constant with respect to the same torsionful Bismut connection, i.e. exhibit the HKT geometry. The key observation is that different comple...
Let $G$ be a Cayley graph of a nonamenable group with spectral radius $\rho
The present contribution is the written counterpart of a talk given in Yerevan at the SQS'2019 International Workshop "Supersymmetries and Quantum Symmetries" (SQS'2019, 26 August - August 31, 2019). After a short presentation of various pictographs (O-blades, metric honeycombs) that one can use in order to calculate SU(n) multiplicities (Littlewoo...
We prove that every countably infinite group with Kazhdan's property (T) has cost 1, answering a well-known question of Gaboriau. It remains open if they have fixed price 1.
We provide a simple proof of the Holonomy Theorem using a new Lyndon-Chiswell length function on the Karnofsky-Rhodes expansion of a semigroup. Unexpectedly, we have both a left and a right action on the Chiswell tree by elliptic maps.
We show that the subgroup of the Picard group of a $p$-block of a finite group given by bimodules with endopermutation sources modulo the automorphism group of a source algebra is determined locally in terms of the fusion system on a defect group. We show that the Picard group of a block over the a complete discrete valuation ring ${\mathcal O}$ of...
Geometrically infinite Kleinian groups have non-conical limit sets with the cardinality of the continuum. In this paper, we construct a geometrically infinite Fuchsian group such that the Hausdorff dimension of the non-conical limit set equals zero. For finitely generated, geometrically infinite Kleinian groups, we prove that the Hausdorff dimensio...
We provide a general framework for computing upper bounds on mixing times of finite Markov chains when its minimal ideal is left zero. Our analysis is based on combining results by Brown and Diaconis with our previous work on stationary distributions of finite Markov chains. Stationary distributions can be computed from the Karnofsky--Rhodes and Mc...
Journal of Topology, 15 (2022) 806-814
Let Γ be a discrete group of isometries acting on the complex hyperbolic n-space HCn. In this note, we prove that if Γ is convex-cocompact, torsion-free, and the critical exponent δ(Γ) is strictly lesser than 2, then the complex manifold HCn/Γ is Stein. We also discuss several related conjectures.
