Hebrew University topology and geometry seminar

Abstract: As was discussed in the previous talk by Pavel, the moduli space of stable closed curves admits a carries natural "tautological" vector bundles. Witten's conjecture asserts that the intersection numbers of their characteristic classes (tautological classes) have a rich structure arising from the recursive structure of the compactifications.
In the open case, the above construction of the compactification fails due to the presence of the boundary. We give a defintion of the moduli space of stable marked disks and its tautological bundles, and the associated tautological bundles. If time permits, we will further define the intersection numbers of the tautological classes and show that their generating functions satisfy a system of commuting PDEs.
Based on a joint work with R. Pandharipande and J. Solomon.