1. Preface

   • Ngô Bao Châu

   EditorialNotes 13 February 2014 Pages: 1 - 1

2. Congruent numbers

   • John Coates

   OriginalPaper 15 January 2014 Pages: 3 - 10

3. Recent progress on the Gross–Prasad conjecture

   • Wee Teck Gan

   OriginalPaper 21 February 2014 Pages: 11 - 33

4. Parabolic flows in complex geometry

   • Duong H. Phong

   OriginalPaper 24 January 2014 Pages: 35 - 54

5. Perfectoid spaces and the weight-monodromy conjecture, after Peter Scholze

   • Takeshi Saito

   OriginalPaper 15 January 2014 Pages: 55 - 68

6. The Tate conjecture for K3 surfaces—a survey of some recent progress

   • Vasudevan Srinivas

   OriginalPaper 14 February 2014 Pages: 69 - 85

7. Representation of finite groups: conjectures, reductions, and applications

   • Pham Huu Tiep

   OriginalPaper 22 January 2014 Pages: 87 - 109