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 well-known modular forms.

*Jim Bryan is a candidate for a position in the Department.