This talk will be a partial survey of the first questions in the
complexity theory of geometric topology problems. What is the
complexity, or what are known complexity bounds, for distinguishing
n-manifolds for various n? For distinguishing knots...
For GL(2) over Q_p, the p-adic Langlands correspondence is
available in its full glory, and has had astounding applications to
Fontaine-Mazur, for instance. In higher rank, not much is known.
Breuil and Schneider put forward a conjecture, which...