Démonstration de la conjecture τ

By L. Clozel. 2003

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Manin's and Peyre's conjectures on rational points and adelic mixing (2006, methodology): “The following corollary presents a stronger version of property (τ) of G proved by Clozel [15]:”
Affine linear sieve, expanders, and sum-product (2010, background): “Progress on the general Ramanujan conjectures for G(Q)\G(A) (see [15, 51, 57]) establish Conjecture 1.”
Rational Points on Homogeneous Varieties and Equidistribution of Adelic Periods (2008, background): “The proof in [36] is based on the information on local harmonic analysis of the groups G(Kv) [54] as well as the automorphic theory of G [18], and gives a rate of convergence.”
The subconvexity problem for GL2 (2009, unknown): “Clozel [14].”
Effective equidistribution of S-integral points on symmetric varieties (2007, background): “20 of [25] based on the results of [8] and [43].”
Expansion in perfect groups (2011, unknown): “[55], [18], [40] and [20].”
Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces (2007, methodology): “Clozel [6]; this solution uses a variety of ingredients: the trace formula, prior”