Pure and Applied Mathematics Quarterly

Preface

Cartan–Iwahori–Matsumoto decompositions for reductive groups

From algebraic geometry to machine learning

Mumford’s influence on the moduli theory of algebraic varieties

Brauer groups of involution surface bundles

Stability and applications

A method in deformation theory

Relations in the tautological ring of the moduli space of curves

On Shimura varieties for unitary groups