Will they be looking more into quantum proofing the Monero protocol or Cuckoo Cycle testing etc?
Monero Research Lab Publications MRL-0001 to MRL-0005 have been published.
The difficulty research that Surae was working on is quite extensive, but incomplete.
EDIT: as of November 17th, it appears MRL-0006 will be renamed MRL-0007.
Someone would have to pick it up and run with it, as Surae is basically burnt out on difficulty and has moved on to other challenges:)
A version of MRL-0008 - Ring Multisignature exists but is not published yet.
Additionally to what Clement J. said, there are a lot of potential future reserach tasks on the Monero Design & Development goals, including Research goals on the bottom half of that page.