Đề tài " Gromov-Witten theory, Hurwitz theory, and completed cycles "

There are two enumerative theories of maps from curves to curves. Our goal here is to study their relationship. All curves in the paper will be projective over C. The first theory, introduced in the 19th century by Hurwitz, concerns the enumeration of degree d covers, π : C → X, of nonsingular curves X with specified ramification data. In 1902, Hurwitz published a closed formula for the number of covers,