Speaker：Gerard van der Geer (University of Amsterdam)
Schedule：Tues. & Thur., 9:50-11:25 am, Sept. 5-Oct. 26, 2023
Venue：Lecture Hall C548, Tsinghua University Shuangqing Complex Building A（清华大学双清综合楼A座C548报告厅）
Sept. 29-Oct.6：Mid-Autumn Festival and National Day Holidays
The lectures on Oct. 3 and Oct. 5 will be canceled. Another two lectures will be delivered on Sat., 9:50-11:25 am, Oct. 14 and Oct. 21，in Lecture Hall B725, Shuangqing Complex Building A。
Modular forms appear in many parts of mathematics: for example in number theory, algebraic geometry and mathematical physics. Siegel modular forms are a natural generalization of the usual elliptic modular forms. The course intends to give an introduction to and overview of Siegel modular forms.It treats basic elements like the Satake compactification and Hecke operators,construction methods of modular forms and the relation with the moduli of abelian varieties.In particular we will pay attention to Siegel modular forms of degree 2 and 3 where invariant theory and a cohomological approach using counting curves over finite fields will help making things explicit.
Some acquaintance with elliptic modular forms is useful, but not necessary. Some familiarity with basic notions in algebraic geometry
References to the literature will be given at the beginning of the course.
Gerard van der Geer is professor emeritus at the University of Amsterdam He works in algebraic geometry and arithmetic geometry with emphasis on moduli spaces and modular forms. He worked on Hilbert modular surfaces,curves over finite fields, cycle classes on moduli of abelian varieties and on modular forms. He got a honorary doctorate of the University of Stockholm.
Registration link: https://www.wjx.top/vm/hIyYeIS.aspx#