Uploaded June 2026 | Updated September 2026, 3 days ago
The 25th Midrasha Mathematicae on Groups, Expanders and Codes -- Celebrating Alex Lubotzky's 70th birthday.
Day 1, Session 1
Speaker: Emmanuel Breuillard (Oxford)
Title: Uniform expansion for finite simple groups
Abstract: In bounded rank, finite simple groups of Lie type are believed to admit uniform expansion; this means a lower bound on the spectral gap that depends only on the rank and not on the finite field nor the generating set. I will discuss three theorems towards this that show that uniformity is achieved, away from a small set of exceptions. The proofs rely on new uniform spectral gap and anti-concentration bounds (non-commutative Littlewood-Offord) for random products. This is joint work with Oren Becker.
The 25th Midrasha Mathematicae on Groups, Expanders and Codes -- Celebrating Alex Lubotzky's 70th birthday.
Day 1, Session 1
Speaker: Emmanuel Breuillard (Oxford)
Title: Uniform expansion for finite simple groups
Abstract: In bounded rank, finite simple groups of Lie type are believed to admit uniform expansion; this means a lower bound on the spectral gap that depends only on the rank and not on the finite field nor the generating set. I will discuss three theorems towards this that show that uniformity is achieved, away from a small set of exceptions. The proofs rely on new uniform spectral gap and anti-concentration bounds (non-commutative Littlewood-Offord) for random products. This is joint work with Oren Becker.
