| Speaker: | Emanuel Scheidegger (Augsburg University) |
|---|---|
| Title: | The Yau-Zaslow conjecture and Noether-Lefschetz theory |
| Date (JST): | Wed, Sep 01, 2010, 13:30 - 17:00 |
| Place: | Seminar Room B |
| Abstract: | The Yau-Zaslow conjecture determines the number of certain BPS states in a type II compactification on a K3 surface in terms of a modular form. In other words, it determines the reduced genus zero Gromov-Witten invariants of K3 surfaces in terms of the Dedekind eta-function. Classical intersections of curves in the moduli space of K3 surfaces with Noether-Lefschetz divisors are related to Gromov-Witten theory on 3-folds via these K3 invariants. The classical intersections of these curves and divisors are determined in terms of vector-valued modular forms. The 3-fold invariants are calculated using mirror symmetry. Via a detailed study of a particular Calabi-Yau 3-fold, we prove the Yau-Zaslow conjecture for all curve classes on K3 surfaces. |
| Remarks: | Break 15:00-15:30, Start with (30 minutes) introduction to non-experts. |
