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中科院数学与系统科学研究院

数学研究所

华罗庚数学重点实验室

华罗庚青年数学论坛

综合报告

 

报告人:Prof. Mingmin Shen(University of Amsterdam)

题  目:The integral Hodge conjecture and the rationality problem

时  间:2018.08.20(星期一),10:45-11:45

地  点:数学院南楼N913室

摘  要: We often study a geometric object by understanding the subspaces contained inside it. When the geometric object is algebraically defined, it is particularly interesting to tell when a subspace is also algebraically defined. A linearised version of this question modulo homological equivalence relation becomes: when can we move a subspace "continuously" to another subspace that is algebraically defined? The integral Hodge conjecture says that if the subspace is a Hodge class (which is easy to check), then the answer to the above question is positive. Atiyah and Hirzebruch disproved the integral Hodge conjecture in 1962; but the reason why the conjecture fails is largely a mystery. In this talk, I will explain how this question is related to another important problem in algebraic geometry -- the rationality problem.

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报告人:Prof. Lie FU(Université Claude Bernard Lyon 1)

题  目:Hyper-K?hler varieties and motives

时  间:2018.08.20(星期一),09:30-10:30

地  点:数学院南楼N913室

摘  要: Hyper-K?hler varieties form one type of building blocks of compact K?hler varieties with vanishing first Chern class. They are natural generalizations of K3 surfaces. After giving some examples and presenting some aspects of the beautiful established theory, I will turn to an overview of the on-going active study of their algebraic cycles, or more fundamentally their motives. General conjectural picture as well as exiting progresses will be discussed.

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