# Mahler's conjecture for some hyperplane sections

## TL;DR

This paper applies symplectic methods to make progress on Mahler's conjecture, confirming it for certain hyperplane sections and projections of specific convex bodies like -balls and Hanner polytopes.

## Contribution

It introduces symplectic techniques to verify Mahler's conjecture for hyperplane sections of -balls and Hanner polytopes, advancing understanding in convex geometry.

## Key findings

- Confirmed Mahler's conjecture for hyperplane sections of -balls
- Confirmed Mahler's conjecture for projections of Hanner polytopes
- Applied symplectic methods to convex geometric problems

## Abstract

We use symplectic techniques to obtain partial results on Mahler's conjecture about the product of the volume of a convex body and the volume of its polar. We confirm the conjecture for hyperplane sections or projections of $\ell_p$-balls or the Hanner polytopes.