主持人：朱萌
报告人简介：
席东盟，上海大学理学院教授，国家级青年人才计划入选者，主要研究凸几何与积分几何中的分析问题。主要成果包括：证明了积分几何中Minkowski问题的弱解存在性；完整解决了2维Dar猜想，并建立了2维非对称凸体的log-Brunn-Minkowski不等式；建立了Orlicz Brunn-Minkowski不等式；构造了高斯概率空间中的几何测度，部分解决了高斯Minkowski问题解的存在唯一性。发表论文20余篇，主要成果发表在Comm. Pure Appl. Math.、J. Differential Geom.、Math. Ann.、Adv. Math.、Trans. Amer. Math. Soc.、J. Func. Anal.、Int. Math. Res. Not.等知名期刊。
报告摘要：
While affine isoperimetric inequalities compare affine geometric invariants (such as volumes and affine surface areas), affine geometric measures arise from the variations of these affine invariants. In this talk, we introduce the affine dual Minkowski problem arising from a new variational formula for Lutwak’s dual affine quermassintegrals. This requires the development of new tools of Radon transforms on the Grassmannian. A new affine operator, called the bi-dual intersection body, appears naturally in this process, and we also establish its affine isoperimetric inequalities.
