报告题目：Quasimodular Forms and Mirror Symmetry for Elliptic Curves

时间：2008.6.30（周一）15：00 --- 16：00

地点：闵行校区数学楼报告厅

主讲人：Noriko Yui教授 (加拿大Queen’s University, Kingston)

内容简介:

    We look into the formula, due to Douglas and Dijkgraaf, on the generating function, Fg(q), of the number of simply ramified covers of genus g≥1 over a fixed elliptic curve with marked points. Their result is that Fg(q) is a quasimodular form of weight 6g − 6 on the full modular group PSL(2,Z). There are two ways of computing Fg(q): the fermionic count and the bosonic count. The fermionic counting is a mathematical treatment, and we will give a mathematical proof to the formula. On the other hand, the bosonic counting rests on physical arguments, which involves path integrals on trivalent Feynman diagrams. We will compute Fg(q) for small genera with bosonic count. This establishes the mirror symmetry prediction for elliptic curves for small genera. When genus g gets bigger, inductive structures in Feynman diagrams might shed light on the calculations of Fg(q).