Volume 189, Issue 1 – January 2019

The first stable homotopy groups of motivic spheres

Pages 1-74 by Oliver Röndigs, Markus Spitzweck, Paul Arne Ostvær

Sharp phase transition for the random-cluster and Potts models via decision trees

Pages 75-99 by Hugo Duminil-Copin, Aran Raoufi, Vincent Tassion

Nonuniqueness of weak solutions to the Navier-Stokes equation

Pages 101-144 by Tristan Buckmaster, Vlad Vicol

Joint equidistribution of CM points

Pages 145-276 by Ilya Khayutin

Macdonald-positive specializations of the algebra of symmetric functions: Proof of the Kerov conjecture

Pages 277-316 by Konstantin Matveev

Errata: PRIMES is in P

Pages 317-318 by Manindra Agrawal, Neeraj Kayal, Nitin Saxena