So far the closest you get to research is the progress through copper -> iron -> mithril
I have not figured out what triggers the progress through the metals.
Maybe it is hard-coded to occur at specific times in the game?
I did try a game where I almost did nothing, except trade with the trader and fullfilling requests from the king.
An almost end of that game screen-shot:
You can maybe see, that strategy can keep up with the usual building up the colony!
As the pricing is at the merchant, then income made at market speculation can keep up with mining for the resources!
I thought it was nescessary to dig down to progress through the copper -> iron -> mithril ladder, but that game did show it happens all by itself.
I did an experiment afterwards, where I just did focus at digging down to the mithril, and I thus managed to have mithril weapons when still at the copper stage.
So it is possible to get ahead of the progress, that is why I think it is hard-coded in some way.