Volume 184, Issue 2 – September 2016

## Extremal results for random discrete structures

Pages 333-365 by Mathias Schacht

## Combinatorial theorems in sparse random sets

Pages 367-454 by D. Conlon, W. T. Gowers

## Imaginary geometry III: reversibility of $\mathrm{SLE}_\kappa$ for $\kappa \in (4,8)$

Pages 455-486 by Jason Miller, Scott Sheffield

## Birational boundedness for holomorphic symplectic varieties, Zarhin’s trick for $K3$ surfaces, and the Tate conjecture

Pages 487-526 by François Charles

## An integrable deformation of an ellipse of small eccentricity is an ellipse

Pages 527-558 by Artur Avila, Jacopo De Simoi, Vadim Kaloshin

## Rigid inner forms of real and $p$-adic groups

Pages 559-632 by Tasho Kaletha

## Proof of the main conjecture in Vinogradov’s Mean Value Theorem for degrees higher than three

Pages 633-682 by Jean Bourgain, Ciprian Demeter, Larry Guth