Abstract: We will discuss the connection between the classical combinatorial problem of counting ramified coverings of a two-dimensional sphere and intersection theory on the moduli space of holomorphic curves with n marked points. This connection leads to a formula expressing the number of coverings as an integral of some characteristic classes of the moduli space. Applications include a new proof of the Witten conjecture (due to A. Okounkov and R. Pandharipande). Joint work with T. Ekedahl, S. Lando, and A. Vainshtein
This talk will be accessible to graduate students and advanced undergraduate students.