56 citations · 159 across the 18 of their papers we have counts for
23 papers
Presenting a proof of the Kannan-Lovasz-Simonovits conjecture
Pierre Bizeul, Boaz Klartag, Joseph Lehec
Together with Bourgain's slicing problem and the variance conjecture, the Kannan-Lovász-Simonovits (KLS) conjecture has been a driving force for mathematical developments in high d…
On the stochastic proof of the Blaschke-Santaló inequality
Joseph Lehec
In 2024, Courtade, Fathi and Mikulincer gave a proof of the symmetrized Talagrand inequality based on stochastic calculus, in the spirit of Borell's proof of the Prékopa-Leindler i…
Thin-shell bounds via parallel coupling
Boaz Klartag, Joseph Lehec
We prove that for any log-concave random vector in with mean zero and identity covariance, where is a universa…
Affirmative Resolution of Bourgain's Slicing Problem using Guan's Bound
Boaz Klartag, Joseph Lehec
We provide the final step in the resolution of Bourgain's slicing problem in the affirmative. Thus we establish the following theorem: for any convex body $K \subseteq \mathbb{R}^n…
Isoperimetric inequalities in high-dimensional convex sets
Bo'az Klartag, Joseph Lehec
These are lecture notes focusing on recent progress towards Bourgain's slicing problem and the isoperimetric conjecture proposed by Kannan, Lovasz and Simonovits (KLS).
Bourgain's slicing problem and KLS isoperimetry up to polylog
Bo'az Klartag, Joseph Lehec
We prove that Bourgain's hyperplane conjecture and the Kannan-Lovász-Simonovits (KLS) isoperimetric conjecture hold true up to a factor that is polylogarithmic in the dimension.