Current research topics in tree automata
Here is a short list of authors that work on the connections between tree automata, logic and databases. For each author, I will just give one paper, but many more can be found on the respective web pages of these authors.

[1] Luc Segoufin

FO2(+1,&lt;.~) on data trees, data tree automata and branching vector addition systems

[2] Nicole Schweikardt

A note on monadic datalog on unranked trees

[3] Mikołaj Bojańczyk

Automata for Data Words and Data Trees.

You may also check Georg Gottlob's work