Kim Stanley Robinson's newest novel 2312 shares a lot of themes with his classic Mars Trilogy. Are they set in a shared universe?
No they are not set in the same Universe, though they may share similar landmarks.
From the Tor website:
It was a pleasant surprise to discover that Robinson actually starts his new novel 2312 in Terminator, the moving city on Mercury, taking the concept from Blue Mars (and, I later discovered, from another novel and short story) and using it as a building block for what may be his most ambitious novel to date: a future history of the solar system, set exactly 300 years into our future. However, one thing should be explained right from the start: despite the similarity of the city on Mercury, 2312 is actually set in a completely different timeline from the Mars trilogy, one in which Mars took a different path. So: a standalone novel, not a sequel. --Tor.com
Yes, I think they are! Mars is referred as "the great revolutionaries", and having a "single planetary government and an economic system variously labeled socialist, communist, utopian, democratic-state-anarchic, syndicalist, worker cooperative, libertarian socialist". Since Blue Mars ends around the year 2200, it could mean that 2312 is set in a universe at least very similar.
But there is a clue that ties it strongly to the Mars Trilogy (spoilers):
When Wahram and Swan are floating in space after abandoning the ETH Mobile, she remembers an old Martian song:
I floated thinking of Peter
Sure I would be saved
But the stories lie
I'm left to die
Black space will be my grave
This most probably refers to Peter Clayborne, who in 2061 was riding a space elevator when it was destroyed by rebels and had to jump from it. He spent some time orbiting Mars and was rescued by chance by a rebel ship.
Same same but different
There are major differences in the described terraforming approach for Mars in 2312, most notably the use of a soletta as the primary mechanism for high-speed terraforming - creating canals across the whole planet. As we know, this approach was tried in the Mars Trilogy but never ran for long as it was such an easy target for malcontents to throw rocks at. KSR has used 2312 to play with some conflicting 'alternative timeline' ideas he had on Martian terraforming. The overall effect is very similar, he's just tried out some new ideas and approaches.
Notably Aurora also touches on Mars but there his alternative timeline is much more pessimistic - very far removed from the Mars of the trilogy.
They are not in the same timeline/universe. Kim Stanley Robinson has clarified this in an interview.
BUT: After having read the first 200 pages of 2312 I dare say that while some details, ideas and developments differ from the Mars trilogy timeline a lot of stuff fits very well. My point being that you will recognise a lot of stuff, and a lot of the state of affairs and developments in 2312 immediately makes sense if you have read the Mars trilogy before. Even if some things are different you can easily spot those differences and put them in a whole bunch of context.
Somebody who reads 2312 first will probably have a much harder time getting into the universe, understanding it and building a mental image of how humanity got to that point. Of course, you can just accept things as they are presented and not worry too much about that.