Criterion for Cannon's Conjecture

The Cannon Conjecture from the geometric group theory asserts that a word hyperbolic group that acts effectively on its boundary, and whose boundary is homeomorphic to the 2-sphere, is isomorphic to a Kleinian group. We prove the following Criterion for Cannon's Conjecture: A hyperbolic group $G$ (that acts effectively on its boundary) whose boundary is homeomorphic to the 2-sphere is isomorphic to a Kleinian group if and only if every two points in the boundary of $G$ are separated by a quasi-convex surface subgroup. Thus, the Cannon's conjecture is reduced to showing that such a group contains "enough" quasi-convex surface subgroups.Comment: Revised versio

On the Forelli-Rudin projection theorem

Motivated by the Forelli--Rudin projection theorem we give in this paper a criterion for boundedness of an integral operator on weighted Lebesgue spaces in the interval $(0,1)$. We also calculate the precise norm of this integral operator. This is the content of the first part of the paper. In the second part, as applications, we give some results concerning the Bergman projection and the Berezin transform. We derive a generalization of the Dostani\'{c} result on the norm of the Berezin transform acting on Lebesgue spaces over the unit ball in $\mathbf{C}^n$.Comment: to appear in Integral Equations and Operator Theor

Semi-norms of the Bergman projection

It is known that the Bergman projection operator maps the space of essentially bounded functions in the unit ball in the d-dimensional complex vector space onto the Bloch space of the unit ball. This paper deals with the various semi-norms of the Bergman projection. We improve some recent results.Comment: to appear in Computational Methods and Function Theor

It’s complicated: a timeline of Australia–Iran relations in a historical perspective

This paper seeks to contextualise Australia’s bilateral relationship with the Islamic Republic of Iran upon the 45th anniversary of diplomatic relations, and at a time when the potential for military conflict is escalating.It canvasses key milestones and events in the bilateral relationship from 1945 to the present. It argues that one of the key continuities in the post-1945 relationship has been the difficulty involved in balancing what has traditionally been a relatively strong bilateral trade relationship with Australia’s broader non-proliferation and global security interests.  Concern over the nuclear program and state-sponsored terrorism in recent years has shifted the balance in favour of a focus on security issues and, consequently, towards the position of Australia’s key partners (especially the United States (US), United Kingdom (UK), Canada and the European Union (EU)) on sanctions. This ‘rebalance’ will only be sharpened (and the scope to follow a more independent policy diminish) if Iran continues down the nuclear path and the likelihood of a military solution increases. Iran’s continuing resistance to provide appropriate assurances about the objectives of its nuclear program is increasing inter-state tensions in the volatile Middle East region, prompting Israel to strengthen its military capacities in the lead-up to the potential conflict. &nbsp

Non-realizability of the Torelli group as area-preserving homeomorphisms

Nielsen realization problem for the mapping class group $\text{Mod}(S_g)$ asks whether the natural projection $p_g: \text{Homeo}_+(S_g)\to \text{Mod}(S_g)$ has a section. While all the previous results use torsion elements in an essential way, in this paper, we focus on the much more difficult problem of realization of torsion-free subgroups of $\text{Mod}(S_g)$. The main result of this paper is that the Torelli group has no realization inside the area-preserving homeomorphisms.Comment: 22 pages, 5 figure