Speaker: Prof. Gerard van der Geer (University of Amsterdam)
Schdule: Every Tue & Thur 19:20-20:55 2020-10-13~12-3
Zoom ID: 849 963 1368 Password: YMSC
Siegel modular forms are a natural generalization of elliptic modular forms. These modular forms play an increasingly important role in number theory, algebraic geometry and mathematical physics. The course gives an introduction to and overview of Siegel modular forms. Besides basic topics like the Satake compactification, Hecke operators, and modular forms associated to lattices, we discuss the relation with the moduli of abelian varieties. We also treat the construction of Siegel modular forms of degree 2 and 3 via invariant theory, a cohomological approach using counting curves over finite fields, and congruences.
Some acquaintance with elliptic modular forms is useful, but not really necessary. Some familiarity with basic notions in algebraic geometry is assumed.
References to the literature will be given at the beginning of the course.