Bourgain's hyperplane conjecture

For $u\in\partial B_2^n$, define $u^\perp=\{x\in\mathbb{R}^n:\langle x,u\rangle=0\}$. For a convex body $K\subseteq\mathbb{R}^n$, let $b(K)=\int_K x\,dx/\lvert K\rvert$ be its barycenter. Bourgain's hyperplane conjecture. There is a universal constant $c>0$ such that, for every $n\geq2$ and every convex body $K\subseteq\mathbb{R}^n$ with $b(K)=0$ and $\lvert K\rvert=1$,

$$\max_{u\in\partial B_2^n}\lvert K\cap u^\perp\rvert\geq c.$$

This is also called the slicing conjecture. The supplied text states that it is equivalent to a universal bound on the isotropic constant and that it remains unresolved.