Entropy, Isotropic Constant and Mahler's Conjecture

Explore a 56-minute lecture on the relationship between entropy, isotropic constant, and Mahler's conjecture presented by Matthieu Fradelizi at the Hausdorff Center for Mathematics. Delve into Bo'az Klartag's work using projective transformations to show how the isotropic constant of a convex body with minimal volume product relates to its volume product. Discover how a strong form of the slicing conjecture implies Mahler's conjecture. Examine the adaptation of these ideas to log-concave functions, introducing additional movements to achieve analogous results. Learn about the importance of choosing the suitable version of the isotropic constant involving entropy for these results to hold. Compare various strong forms of the slicing conjecture for s-concave functions. Gain insights from this collaborative work with Francisco Marin Sola, expanding your understanding of geometric functional analysis and convex geometry.