Abstract:
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.