Mathematics

Teichmueller curves are complex geodesics in the moduli
space of curves with respect to the Kobayashi metric. As
such, a Teichmueller curve in genus 2 moduli space naturally
parametrizes a family of Kummer K3 surfaces. We will discuss
the geometry of such a family of K3 surfaces arising from
Teichmueller curves, with special emphasis on the variation of
Hodge structure and mirror symmetry. Time permitting, we will
talk about 'attractive' K3 surfaces, which are special fibers of
this family, that provide a fascinating link between the arithmetic
theory of complex multiplication and black holes in type IIB string
theory compactified on the product of a K3 surface with an elliptic
curve (This is ongoing work with Atish Dabholkar (ICTP)).