On sets invariant under the action of the diagonal group

By Elon Lindenstrauss, Barak Weiss. Ergodic Theory and Dynamical Systems, 2001

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Invariant measures and the set of exceptions to Littlewood's conjecture (2006, background): “In [21] a complete classification of the possible algebraic μ is given.”
Minkowski’s Conjecture, Well-Rounded Lattices and Topological Dimension (2005, background): “For more on compact A-orbits, minimal sets and totally real fields, see [ LW ] and [Oh].”
Invariant measures and arithmetic quantum unique ergodicity (2006, methodology): “I have had the good fortune to collaborate with several people about topics related to this work: in rough chronological order, with David Meiri and Yuval Peres [LMP99], Barak Weiss [ LW01 ], Jean Bourgain [BL03], Francois Ledrappier [LL03], Klaus Schmidt [LS03] and Manfred Einsiedler [EL03], and ha”
The distribution of periodic torus orbits on homogeneous spaces (2006, methodology): “8 is that in [25, 45] the set Y is assumed to be of the form Y = xH for some x ∈ Γ\G (in which case assumption (3) is automatic unless Y = yL).”
Rigidity of measures—The high entropy case and non-commuting foliations (2005, unknown): “Every root λ of G can be restricted to the image of the derivative Dα (with base point 0 ∈ Rk), and induces in this way a linear map λ(α) = λ ◦Dα : Rk → C.”