D. Zvonkine's talks


  1. Moduli spaces of curves and their tautological rings.

    2. M_{g,n}, examples of M_{0,n}, M_{1,1}, M_{2,0}. A few words about orbifolds. Stable curves, the Deligne-Mumford space Mbar_{g,n}, examples.
    Tautological classes: psi-classes, kappa-classes, lambda-classes, boundary divisors. Some elementary computations.

  2. The strata algebra and tautological relations.

    3. Stable graphs and how to multiply them. Definition and examples of tautological relations.

  3. Cohomological field theories.

    4. Axioms of a CohFT. Example of Gromov-Witten theories, Moduli space of r-spin curves, its compactification, Witten's r-spin class, check that it's a CohFT.

  4. Frobenius manifolds.

    5. Frobenius manifolds as genus 0 part of CohFT and as a differential geometric structure (family of fusion algebras).
    GW-potential of a Frobenius manifold. Shift of CohFTs. Semi-simple CohFTs.

  5. Givental's group action on CohFTs and Teleman's classification of semi-simple CohFTs.

  6. Pixton's relations.

    7. Putting everything together for the proof. An explicit expression for Witten's 3-spin class and sample computations of tautological relations.