March 28, Wednesday, 15:30, room 211

Artem Galkin

Mahler conjecture and Blaschke-Santalo inequality

Mahler volume of a centrally symmetric convex body is a dimensional quantity that is associated with the body and is invariant under linear transformations. It is known that the shapes with the largest possible Mahler volume are the balls and solid ellipsoids; this is now known as the Blaschke–Santaló inequality. The still-unsolved Mahler conjecture states that the minimum possible Mahler volume is attained by a hypercube. I will make a brief overview of the known results obtainted towards the complete solution of Mahler conjecture and provide the proof of the Blaschke-Santalo inquality for symmetric convex bodies. If time permits, we will cover some stability estimates and discuss the relationship between Mahler conjecture and Faber-Krahn inequality for the Cheeger constant.