一、报告题目：Curved Kakeya problems

二、报告人：席亚昆 教授

三、时  间：2026年4月29日（周三）14:00—15:00

四、地  点：A4-305

报告摘要：We study curved Kakeya sets defined by Hormander phase functions. We show that the analysis of curved Kakeya sets arising from translation-invariant phase functions under Bourgain's condition, as well as Nikodym sets on manifolds with constant sectional curvature, can be reduced to the study of standard Kakeya sets in Euclidean space. Combined with the recent breakthrough of Wang and Zahl, our work establishes the Nikodym conjecture for three-dimensional manifolds with constant sectional curvature. On the other hand, we show that for generic positive definite Hormander phase functions, the associated curved Kakeya sets have Hausdorff dimension strictly greater than (n+1)/2, surpassing the Kakeya compression threshold.

报告人简介：席亚昆，浙江大学数学科学草榴社区百人计划研究员、博士生导师，国家级青年人才。主要从事经典调和分析及流形上的调和分析研究，相关成果发表于 Camb. J. Math.、Amer. J. Math.、Proc. Lond. Math. Soc.、Comm. Math. Phys.、Peking Math. J.、Adv. Math.、Trans. Amer. Math. Soc.、J. Funct. Anal.、Pure Appl. Anal. 等国际一流期刊。主持国家重点研发计划“青年科学家”项目、国家自然科学基金面上项目及浙江省自然科学基金杰出青年基金。

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