Pierre Bizeul

Preprint Oct 2026

Presenting a proof of the Kannan-Lovasz-Simonovits conjecture

Together with Bourgain's slicing problem and the variance conjecture, the Kannan-Lov\'asz-Simonovits (KLS) conjecture has been a driving force for mathematical developments in high dimensional geometry in recent decades. We present here a proof of this conjecture. The crucial step in the proof is the very recent criter...

Pierre Bizeul, Bo'az Klartag, Joseph Lehec · 5 citations · ⚡2

Preprint Jul 2026

Optimal MM* bounds for convex bodies

Let $K\subset\R^n$ be a convex body in isotropic position. We prove the optimal mean-width estimate \[ M^*(K)\leq C\sqrt{n\log n}. \] The main new ingredient is a geometric inequality relating the Gaussian mean of the support function to its mean under the uniform measure on $K$, obtained through a heat-flow argument....

Pierre Bizeul · 10 citations · ⚡4

Preprint Jul 2026

Optimal $MM^*$ bounds for convex bodies

Let $K\subset\R^n$ be a convex body in isotropic position. We prove the optimal mean-width estimate \[ M^*(K)\leq C\sqrt{n\log n}. \] The main new ingredient is a geometric inequality relating the Gaussian mean of the support function to its mean under the uniform measure on $K$, obtained through a heat-flow argument....

Pierre Bizeul · 7 citations · ⚡3