Vol. 39 No. 1, 2014

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Lectures at the Annual Meeting 2013
of the Vietnam Institute for Advanced Study in Mathematics

Preface
Ngô Bao Châu

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1

Congruent numbers
John Coates

3

Recent progress on the Gross–Prasad conjecture
Wee Teck Gan

11

Parabolic flows in complex geometry
Duong H. Phong

35

Perfectoid spaces and the weight-monodromy conjecture, after Peter Scholze
Takeshi Saito

55

The Tate conjecture for K3 surfaces—a survey of some recent progress
Vasudevan Srinivas

69

Representation of finite groups: conjectures, reductions, and applications
Pham Huu Tiep

87