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Георгий Борисович Шабат

Пересечения в пространствах модулей кривых, часть 2

Программа курса

  1. The spaces Mg;N (C) and their combinatorial models
    1.0. Stable curves
    1.1. Metrized ribbon graphs
    1.2. Strebel-Penner-Kontsevich-... theory
    1.3. Combinatorial interpretation of the brations Li; their Chern classes
    1.4. Volumes of moduli spaces and their Laplace transforms
    1.5. Discrete version of the theory and arithmetic
  2. Kontsevich's proof of Witten's conjecture
    2.0. The generating function for the intersection numbers
    2.1. Matrix integrals
    2.2. The main Kontsevich's combinatorial identity
    2.3. Matrix Airy function and its asymptotic expansion
    2.4. Applications, generalizations and new ideas
  3. 3. Other proofs of Witten's conjecture
    3.0. Algebro-geometric proof by Lando-Kazarian
    3.1. On the Mirzahani's theory
    3.2. On the Okun'kov-Pandaripande and Kim-Lu proofs