Seminar "Combinatorics of invariants". Speaker: S.K.Lando
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Hurwitz numbers
Simple Hurwitz numbers enumerate decompositions of permutations into products of transpositions. They are closely related to enumerating spanning trees and spanning forests in graphs and embedded graphs.
More general Hurwitz numbers enumerate decompositions of permutations into permutations of prescribed cycle types. They also enumerate rational functions of a complex variable, with prescribed ramification types over given points. Various species of Hurwitz numbers play a key role in several modern theories including integrable systems, topological recursion, moduli spaces of algebraic curves.
The talk will be devoted to a discussion of the simplest manifestations of Hurwitz numbers.