题目：Some Open Problems in Geometric Tomography and Convex Geometry, including the Hyperplane and Mahler Conjectures

报告人：Prof. Richard Gardner （Western Washington University）

地点：宁静楼104室

时间：2024年5月29日 10:00-11:30

摘要: The talk focuses on just a few of the 66 problems stated in my book Geometric Tomography that are among those still open. The selected problems happen to fall within convex geometry. The first topic is Nakajima's problem on constant width and brightness and several problems related to it. After this, a conjectured inequality concerning affine quermassintegrals will be discussed. The main part of the talk addresses Bourgain's hyperplane conjecture and Mahler's conjecture, which have great significance not only for convex geometry, but for mathematics as a whole. A fairly comprehensive survey of these two important questions will be attempted, including their relationship to each other and to many other open conjectures from diverse areas of mathematics. The talk is designed to be accessible to students and non-specialists.

All are welcome!