BLISS Seminar: Kannan-Lovasz-Simonovitz Conjecture
Seminar | October 16 | 3-4 p.m. | 540 Cory Hall
Yin-Tat Lee, UW Seattle
Kannan-Lovasz-Simonovitz (KLS) conjecture asserts that the isoperimetric constant of any isotropic convex set is uniformly bounded below.
It turns out that this conjecture implies several well-known conjectures from multiple fields: (Convex Geometry) Each unit-volume convex set contains a constant area cross section. (Information Theory) Each isotropic logconcave distribution has O(d) KL distance to standard Gaussian distribution. (Statistics) A random marginal of a convex set is approximately a Gaussian distribution with 1/sqrt(d) error in total variation distance. (Measure Theory) Any function with Lipschitz constant 1 on an isotropic logconcave distribution is concentrated to its median by O(1).
In this talk, we will discuss the latest development on the KLS conjecture.
Joint work with Santosh Vempala.