Colloquium
3:30 p.m., Wednesday, (Feb. 14)
West Mall Annex 216, (PIMS Seminar Room, 1933 West Mall)
Jim Bryan*
Tulane University, New Orleans, LA
The enumerative geometry of K3 surfaces and modular forms
In the last fifteen years, mathematicians and physicists have
discovered surprising connections between the physics of string
theory and the enumerative algebraic geometry of complex
projective manifolds. In this talk I will explain the sorts
of questions that enumerative geometry asks through many
elementary examples. I will explain what K3 surfaces are
and formulate the enumerative geometry problems for them.
I will sketch how to obtain the complete solution to these
questions. The answer turns out to be surprising and quite
beautiful: the numbers are given as the coefficients in the
Fourier expansions of wellknown modular forms.
*Jim Bryan is a candidate for a position in the Department.
