Number Theory Seminar

Tuesday 8 May 2007, MR13

Quasimodular forms and mirror symmetry for elliptic curves
Noriko Yui (Queen's University, Kingston Canada/DPMMS )


     We look into the formula, due to Douglas and Dijkgraaf, on the generating function, F_g(q), of the number of simply ramified covers of genus g>=1 over a fixed elliptic curve with marked points. Their result is that F_g(q) is a quasimodular form of weight 6g-6 on the full modular group PSL_2(Z).

There are two ways of computing F_g(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 F_g(q) for small genera with bosonic count.

Last modified on 20/1/07.

Comments/corrections to Tim Dokchitser