4 papers
Uniform expansion in finite groups of Lie type
Oren Becker, Emmanuel Breuillard
We prove that finite simple groups of bounded rank and with prime have uniform expansion, that is, the family of all the Cayley graphs forms a family of (two-sided) expa…
Uniform spectral gaps, non-abelian Littlewood-Offord and anti-concentration for random walks
Oren Becker, Emmanuel Breuillard
We show that random walks on semisimple algebraic groups do not concentrate on proper algebraic subvarieties with uniform exponential rate of anti-concentration. This is achieved b…
Word maps and random words
Emmanuel Breuillard, Itay Glazer
We discuss some recent results by a number of authors regarding word maps on algebraic groups and finite simple groups, their mixing properties and the geometry of their fibers, em…
Undecidability of the stabilizer and zero-in-the-corner problems for matrix groups
Emmanuel Breuillard, Georgi Kocharyan
The show that the upper-left-corner problem and upper-right-corner problem for matrix groups with rational entries are undecidable. To reach this aim, we answer a question of Dixon…