BLISS Seminar: Kannan-Lovasz-Simonovitz Conjecture

Seminar | October 16 | 3-4 p.m. | 540 Cory Hall

 Yin-Tat Lee, UW Seattle

 Electrical Engineering and Computer Sciences (EECS)

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.