Everytopic Seminar

 October 23rd, 2007, 1:40 pm – 3:00pm, Goldsmith 226



Title: Fourier-Mukai numbers of K3 surfaces and class numbers

Speaker: Bong Lian, Brandeis University






I will define Fourier-Mukai numbers following S. Mukai, and show that

they can be computed using elementary group theory and the theory of

lattices. I will give an explicit formula for these numbers in terms

of the Picard lattice of a K3 surface (which I will define), and then

explain some of its applications. One of them relates Fourier-Mukai

numbers to class numbers of real quadratic fields of prime

discriminants. Another application is a solution to an old problem of

T. Shioda about abelian surfaces. This is joint with S. Hosono, K.

Oguiso, and S.T. Yau.