Title: The shape of the universe
Abstract: String theory predicts that our universe is a 10-dimensional space. This includes the, by now, classical 4-dimensional spacetime and a somewhat mysterious additional 6 dimensions. These extra dimensions are extremely tiny--which is probably why it took so long to even theorize about them, but the physical equations predict their existence and that this additional 6-dimensional space is best approximated by certain algebro-geometric objects known as Calabi-Yau spaces. I will talk about these and related spaces and their significance in some purely mathematical questions which are central to current research in algebraic geometry and which nevertheless might be interesting to the physicists.