The sharp simplex conjecture for isotropic constants
What the paper claims, in its own words
Proves that simplices uniquely maximize the isotropic constant among convex bodies in every dimension, resolving the strong isotropic constant conjecture. Also establishes the sharp entropy lower bound for log-concave probability densities, with equality precisely for invertible affine images of products of one-sided exponential laws.
The plain-language explainer for this entry is still coming.