2 problems

KLS conjecture. The Poincaré constant satisfies $C_{\mathsf{PI}}(\pi)=\mathcal{O}(1)$, uniformly over all dimensions and isotropic logconcave probability measures.

Let $q$ be a logconcave density on a finite-dimensional Euclidean space, with covariance matrix $A$. The KLS conjecture. The KLS constant of every isotropic logconcave density, in…