Kiran Kedlaya <br>

Title: Sato-Tate groups of abelian varieties and other
motives <br>
Abstract:
The Sato-Tate conjecture for elliptic curves, now proved over
totally
real fields, predicts the distribution of the characteristic
polynomials
of Frobenius at "random" primes. There is a trichotomy between
elliptic
curves with complex multiplication (CM)  over the base field,
with CM
over a large field, or without CM. We describe an analogous
conjecture
for abelian surfaces which predicts a corresponding
distribution in
terms of a certain compact Lie group (the Sato-Tate
group). This group
can take any of 52 different forms. Joint work with Francesc
Fite,
Victor Rotger, and Drew Sutherland.