TITLE: Is Lusztig's conjecture solved?
QUESTION [12 upvotes]: What I said is Lusztig's conjecture about representation of quantum group at root of unity and representation of Lie algebra at positive characters.
It seems that Andersen-Jantzen-Soergel ever wrote a book on this conjecture. 
Is it solved? Any recent development? I am looking for reference talking about it. 
Thank you

REPLY [20 votes]: Geordie Williamson has found counterexamples to Lusztig's conjecture: 
http://people.mpim-bonn.mpg.de/geordie/Torsion.pdf
Apparently, any bound on the largest prime that breaks Lusztig's conjecture must be at least proportional to $n\log n$, and this is probably still far too optimistic; I think it's now believed that you'll need an exponential bound.