Related papers: The Baum-Connes conjecture with coefficients for w…

We prove that, for a finitely generated group hyperbolic relative to virtually abelian subgroups, the generalised word problem for a parabolic subgroup is the language of a real-time Turing machine. Then, for a hyperbolic group, we show…

In this paper we study the commensurability of hyperbolic Coxeter groups of finite covolume, providing three necessary conditions for commensurability. Moreover we tackle different topics around the field of definition of a hyperbolic…

Using the concepts of Hyperbolic Classification of Natural Numbers, Essential Regions and Goldbach Conjecture Function we prove that the existence of a proof of the Goldbach Conjecture in First-Order Arithmetic would imply the existence of…

Comment on recent claims by Sornette and Zhou: D. Sornette and W. Zhou, Quantitative Finance 2 (6), 468-481 (2002); Evidence of a Worldwide Stock Market Log-Periodic Anti-Bubble Since Mid-2000, cond-mat/0212010; Renormalization Group…

This is an extended abstract for the conference "Microlocal2011 : Microlocal Methods in Mathematical Physics and Global Analysis Universitat Tubingen, June 14 - 18, 2011"

Rigorous justification of the Hubbard-Stratonovich transformation for the Pruisken-Sch\"afer type of parameterisations of real hyperbolic O(m,n)-invariant domains remains a challenging problem. We show that a naive choice of the volume…

Minor changes in the exposition and small corrections on the previous version.

In this short note, we prove that the restriction conjecture for the (hyperbolic) paraboloid in $\mathbb{R}^d$ implies the $l^p$-decoupling theorem for the (hyperbolic) paraboloid in $\mathbb{R}^{2d-1}$. In particular, this gives a simple…

In this paper we formulate a conjecture which is a strengthening of an extension theorem of Bakonyi and Timotin for positive definite functions on the free group on two generators. We prove that this conjecture implies Connes' embedding…

We associate a non-commutative $C^*$-algebra with any locally finite simplicial complex. We determine the $K$-theory of these algebras and show that they can be used to obtain a conceptual explanation for the Baum-Connes conjecture.

Let $(M, \dr M)$ be a 3-manifold with incompressible boundary that admits a convex co-compact hyperbolic metric. We consider the hyperbolic metrics on $M$ such that $\dr M$ looks locally like a hyperideal polyhedron, and we characterize the…

Carrier graphs of groups representing subgroups of a given relatively hyperbolic groups are introduced and a combination theorem for relatively quasi-convex subgroups is proven. Subsequently a theory of folds for such carrier graphs is…

These notes cover the contents of three survey lectures held at the ICTP Trieste Summer school on High dimensional manifold theory 2001. They introduce techniques coming from the theory of operator algebras. We will focus on the basic…

We show that the statement analogous to the Mumford-Tate conjecture for abelian varieties holds for 1-motives on unipotent parts. This is done by comparing the unipotent part of the associated Hodge group and the unipotent part of the image…

We obtain new lower and upper bounds for probabilities of unions of events.These bounds are sharp. They are stronger than earlier ones. General bounds maybe applied in arbitrary measurable spaces.We have improved the method that has been…

We prove a conjecture of R. Schwartz about the type of some complex hyperbolic triangle groups.

We explore the combination theorem for a group G splitting as a graph of relatively hyperbolic groups. Using the fine graph approach to relative hyperbolicity, we find short proofs of the relative hyperbolicity of G under certain…

We present the status of the Farrell-Jones Conjecture for algebraic K-theory for a group G and arbitrary coefficient rings R. We add new groups for which the conjecture is known to be true and study inheritance properties. We discuss new…

These are notes based on a series of talks that the author gave at the "Interactions between hyperbolic geometry and quantum groups" conference held at Columbia University in June of 2009.

This paper is an extended version of math.OA/0601528 where we point out and remedy a gap in the proof by P. Julg and G. Kasparov of the Baum-Connes conjecture for discrete subgroups of SU(n,1). In particular, here we explain in details why…