On the spectral gap for finitely-generated subgroups of SU(2)

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RIGIDITY FOR VON NEUMANN ALGEBRAS (2017, result): “This result is due to Bourgain and Gamburd for G = SO(3) Bourgain and Gamburd [2008], and to Benoist and de Saxcé in general Benoist and de Saxcé [2016]. In joint work with Boutonnet and Salehi-Golsefidy, we have shown that the same holds if G is an arbitrary connected simple Lie group Boutonnet, Io”
A spectral gap theorem in simple Lie groups (2014, methodology): “Using the discretized Product Theorem proved in [14] and the techniques developped by Bourgain and Gamburd in [4] for the group SU(2), we prove the following theorem.”
Notes on Thin Matrix Groups (2012, methodology): “That the expansion property might continue to hold for thin groups was first suggested by Lubotzky [1993].”
On the diameter of permutation groups (2011, background): “The paper [Hel08] initiated a period of intense activity [BG08a], [BG08b], [Din11], [BGS10], [Hel11], [GH], [Var12], [BGS11], [PS10], [BGT11], [GH10], [GV12](1) on the diameter problem and the related problem of expansion properties of Cayley graphs.”
Random walks in compact groups (2012, background): “We say that a profinite group G is (c, α)-quasirandom if for every irreducible unitary representation π of G, we have dimπ ≥ c[G : Ker(π)]α.”