报告人：李媛媛（西湖大学）

报告时间：2026年6月10日（星期三）14：00-15：30

报告地点：东三十二楼216室

报告摘要：We settle the three-dimensional Mahler conjecture for arbitrary convex bodies. Prior to this work, the Mahler conjecture for arbitrary convex bodies had remained open in all dimensions \(n\geq 3\) since Mahler's original work in 1938. More precisely, for every convex body \(K\subset \mathbb R^3\), we prove the sharp inequality\[|K|\, |K^{s(K)}|\geq \frac{64}{9},\]where  \(K^{s(K)}\) denotes the polar of \(K\) with respect to Santal\'o point \(s(K)\). The lower bound is attained by simplices; among polytopes, these are the only equality cases. The key ingredient in our proof is an admissible shadow-system framework, which produces face-lattice-preserving, volume-affine deformations and reduces the problem to a dimension count for the space of admissible speeds. As an application, this framework also yields a purely geometric new proof of the three-dimensional centrally symmetric Mahler inequality, first proved by Iriyeh and Shibata. This is joint work with Shibing Chen (USTC)，Dongmeng Xi(SHU) and Zhe-Feng Xu(SISSA&USTC).

报告人简介：李媛媛，西湖大学博士后，中国科学技术大学博士，师从陈世炳教授与汪徐家教授，在椭圆方程及凸几何方向有突出贡献，尤其近期其与合作者完全解决三维Mahler猜想。

邀请人：张宁