I have a proof that if $n$ is an integer such that $n>1$ and $k$ is any field, then if $g$ is an element of $\mathrm{SL}(n,k)$ of infinite order then the set of all $h$ with the property that $g$ and $h$ generate a free group of rank two is Zariski dense. 


<http://rupertmccallum.com/free_groups.pdf>


I am trying to find out if this result is already known. My former PhD supervisor Michael Cowling has said that it has appeared in a PhD thesis of Tal Poznansky, and I would like to contact Poznansky to see if I am saying anything new, or whether perhaps the method of argument is of some interest, but I have not been able to find Poznansky's email address on-line. 


Does anyone know someone who is knowledgeable about results of this kind who might be able to tell me whether there is anything new here and whether the result is publishable?



ubiquity of free subgroups of special linear groups
I think this is an interesting result with a cool method. By the way, you might want to look at Theorem 2 on page 158 of Borel's "On free subgroups of semisimple groups" (Enseign. Math. (2), 29(1-2):151–164, 1983). Using this and the Ping-Pong lemma, you can prove results that are similar (but not identical) to yours. 


