课程名称：Hodge theory and algebraic cycles

课程学分：2   （课程编号：MA05185，可通过教务系统选课）

授课教师：沈明民   （University of Amsterdam）

授课日期：2020年6月23日-7月15日

上课时间及听课链接：

（Ⅰ） 北京时间周二和周四下午，15:00-18:00：

Topic: USTC: Hodge theory and algebraic cycles (Tue, Thur)

Time: Jun 23, 2020 09:00 AM Amsterdam (北京时间15:00)

          Every week on Tue, Thu, until Jul 16, 2020, 8 occurrence(s)

          Jun 23, 2020 09:00 AM

          Jun 25, 2020 09:00 AM

          Jun 30, 2020 09:00 AM

          Jul 2, 2020 09:00 AM

          Jul 7, 2020 09:00 AM

          Jul 9, 2020 09:00 AM

          Jul 14, 2020 09:00 AM

          Jul 16, 2020 09:00 AM

Join Zoom Meeting

https://uva-live.zoom.us/j/95330239318?pwd=Vk1rZW5rRUpnWWRaTlcrbEtlSW52QT09

Meeting ID: 953 3023 9318

Password: ustcHodge

（Ⅱ） 北京时间周三下午，15:00-17:00：

Topic: USTC: Hodge theory and algebraic cycles (Wed afternoon)

Time: Jun 24, 2020 09:00 AM Amsterdam (北京时间下午15:00)

          Every week on Wed, until Jul 15, 2020, 4 occurrence(s)

          Jun 24, 2020 09:00 AM

          Jul 1, 2020 09:00 AM

          Jul 8, 2020 09:00 AM

          Jul 15, 2020 09:00 AM

Join Zoom Meeting

https://uva-live.zoom.us/j/94225936601?pwd=L1NzWE10UURPb1hZUWZHQWpyN0tDZz09

Meeting ID: 942 2593 6601

Password: ustcHodge

（Ⅲ） 北京时间周三晚上，20:00-22:00：

Topic: USTC: Hodge theory and algebraic cycles (Wed. evening)

Time: Jun 24, 2020 02:00 PM Amsterdam (北京时间20:00)

          Every week on Wed, until Jul 15, 2020, 4 occurrence(s)

          Jun 24, 2020 02:00 PM

          Jul 1, 2020 02:00 PM

          Jul 8, 2020 02:00 PM

          Jul 15, 2020 02:00 PM

Join Zoom Meeting

https://uva-live.zoom.us/j/95743908141?pwd=eEYrQm1aT3V3UFBuT1VTVHJnbEQxQT09

Meeting ID: 957 4390 8141

Password: ustcHodge

课程简介：In 1930's, W. Hodge discovered  that  the  complex  valued  cohomology  groups  of  a  compact  Kahler  manifold  admit  a  canonical  decomposition,  called Hodge decomposition. Such a decompositon endows the cohomology of a compact Kahler manifold an extra structure, which is nowadays called a Hodge structure. Hodge theory plays an important role in algebraic geometry, especially in the study of algebraic cycles. One of the central unsolved problem in mathematics -- the Hodge Conjecture -- arises from such studies. The Hodge conjecture is also one of the seven Millennium Prize Problems.

The goal of this course is to study the cohomology of algebraic varieties from various aspects. (ⅰ) Develop the basics of the Hodge theory; (ⅱ) Classical results concerning the cohomology of algebraic varieties (Lefschetz, Torelli theorems); (ⅲ) Applications in the study of algebraic cycles.

References: 

C. Voisin, Hodge theory and complex algebraic geometry (I, II)

P. Griffiths and J. Harris, Principles of algebraic geometry