Editors' Choice: Proceedings

Founded in 1865, the Proceedings is the flagship journal of the LMS.  Over its long history it has published many significant papers including those by Atiyah, Donaldson, Hardy, Ramanujan, Rayleigh and Turing

More recently, in 2019, a new, independent Editorial Board of international experts was appointed to identify papers of the highest quality and significance across a broad spectrum of mathematics. The aim of these changes was to further elevate the position of the journal and strengthen its position with relation to other top-flight mathematics journals.

Over the last three years the Proceedings Editorial Board have accepted many papers of high-quality and significance.  The Managing Editors, Tim Browning and Oscar Randal-Williams have chosen six such articles to highlight, all of which are free to read online.

Symplectomorphisms with positive metric entropy
Artur Avila, Sylvain Crovisier and Amie Wilkinson
A general and deep result providing a complete answer to an old question of Mañé.

The density of polynomials of degree n over ℤp having exactly r roots in ℚp
Manjul Bhargava, John Cremona, Tom Fisher and Stevan Gajović
Some surprising and down to earth statements about roots of polynomials over ℤp.

Shift-invariance for vertex models and polymers
Alexei Borodin, Vadim Gorin and Michael Wheeler
This paper establishes some highly non-trivial invariance properties for a wide class of integrable models.

Complete Moduli of Cubic Threefolds and their Intermediate Jacobians
Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek and Radu Laza
This paper solves an important algebraic geometry question about the Torelli map from the space of cubic threefolds.

Motivic Chern classes and K-theoretic stable envelopes
László M. Fehér, Richárd Rimányi, Andrzej Weber
An influential paper relating invariants of singular spaces to quantum groups.

Independent sets in hypergraphs with a forbidden link
Jacob Fox and Xiaoyu He
This work provides a solution to a 50-year-old problem of Erdős and Hajnal.