KLS Conjecture (Kannan–Lovász–Simonovits)

Isoperimetric problems for convex bodies and a localization lemma

Ravi Kannan, László Lovász, Miklós Simonovits (1995)

Discrete & Computational Geometry

📍 Section 5, unnumbered “Conjecture” immediately preceding Theorem 5.4, p. 557 (Discrete & Computational Geometry 13 (1995), 541–559).

Bourgain's slicing problem and KLS isoperimetry up to polylog

Bo'az Klartag, Joseph Lehec (2022)

Thin shell implies spectral gap up to polylog via a stochastic localization scheme

Ronen Eldan (2013)

Geometric and Functional Analysis (GAFA)

📍 Section 1 (Introduction), Theorem 1.1 (thin-shell width controls Poincaré constant up to polylog), p. 533.

Eldan's stochastic localization and the KLS hyperplane conjecture: An improved lower bound for expansion

Yin Tat Lee, Santosh S. Vempala (2017)

FOCS 2017

📍 Section 1 (Introduction), Theorem 1.1 (Cheeger constant C_n = O(n^{1/4}), first sub-polynomial bound), p. 2.