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Gromov-Witten invariants of a space X can intuitively be defined as counts of maps
from a genus-g curve into X with certain constraints. In this talk I will talk about
two tools for computing Gromov-Witten invariants. The first of these will be the WDVV
equations, which were used by Kontsevich to determine the number of degree d rational
curves through 3d-1 points in CP^2. The second one are R-matrices, which were used by
Givental and Teleman to recover all-genus invariants from the genus 0, 3 point
invariants. This method is not very widely applicable though: it requires the quantum
cohomology ring of X (which is a deformation of the usual cohomology ring) to be
semi-simple. After overviewing this construction, I will give an example of a
construction of an R-matrix in a more general setting.
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