Updates: letztes: 5.5.99 nächstes: [verantwortlich]
von Montag 5.7.99 bis Freitag 9.7.99
It has been striking that the string theory often inspires new and deep questions in geometry, which may have been hard to imagine from the point of view of classical geometry. The answers to these questions turn out to be surprisingly rich, leading to new theories in mathematics, such as the theory of Quantum cohomology and mirror symmetry. It also provides new insight into geometry of algebraic manifolds.
In this lecture I will discuss sume recent progress on mathematical aspects of Quantum cohomology and mirror symmetry for algebraic manifolds, particularly, Calabi-Yau manifolds. This is also a general introduction to the next two lectures.
This lecture will concern special geometric properties of Calabi-Yau manifolds. These include geometry of moduli spaces and special Lagrangian submanifolds. We will discuss the connection between the T-duality and special Lagrangian cycles. We will also discuss how holomorphic vector bundles arise from special Lagrangian cycles.
In this lecture, we discuss methods of computating quantum cohomology for special algebraic manifolds, such as Calabi-Yau spaces and Fano manifolds. We will also discuss how the computation is related to geometry and mirror symmetry of those spaces. Some unsolved problems may be discussed in the end.