Kudos to Nicolas Bergeron, Paul Gunnells, and Akshay Venkatesh for organizing a wonderfully interesting conference at BIRS on torsion on the homology of arithmetic groups. If you had the bad luck not to be in Banff last week, never fear: they’ve put in an ultra-fancy new recording/streaming system and you can watch most of the talks online. The introductory talks by Frank Calegari and Nicolas are a great place to start.
I was raised to think of torsion classes in homology as a terrifying mystery that one dealt with by tensoring with the rational numbers as quickly as possible. But our knowledge about these things is actually starting to accumulate!
Here’s a puzzle that came up while I was talking to Simon Marshall, whose work makes crucial work of the story about completed cohomology of towers of manifolds that Frank Calegari and Matt Emerton have been steadily telling us.
(remark: everything below is written off the cuff and no details are checked.)