Moduli Spaces and Modular Forms
Student No.:50
Time:【Updated】Time change to Tue. 15:20-17:10/Fri. 13:00-14:50, (up to change; to be decided during the class)
Instructor:Gerard van der Geer  [University of Amsterdam]
Place:Conference Room 1, Floor 1, Jin Chun Yuan West Building
Starting Date:2012-9-25
Ending Date:2012-11-21

Course description:

Moduli spaces, that is, the parameter spaces of algebraic geometric objects like curves, abelian varieties, K3 surfaces, are provided with natural line bundles and vector bundles, like the Hodge bundle. Sections of these bundles are usually called modular forms. These forms not only carry a lot of geometric information, but also a lot of arithmetic information. Elliptic modular forms were already studied in the 19th century by Jacobi, Kronecker, Eisenstein and others and played a very important role in 20th century algebraic geometry and number theory. The course will give an introduction to these topics and will also deal with the higher genus analogues, like vector-valued Siegel modular forms.




A moderate knowledge of algebraic geometry



Reference for the course:

Bruinier, van der Geer, Harder, Zagier: The 1-2-3 of Modular Forms.

Springer Verlag. More references will be given during the course.