1/3 Mathematical Physics of Hurwitz numbers

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1/3 Mathematical Physics of Hurwitz numbers
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Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge number of relations represented in the form of partial differential equations for their generating function. This includes equations of the KP hierarchy, Virasoro-type constraints, Chekhov-Eynard-Orantin-type recursion and others. Only a few of these relations can be derived from elementary combinatorics of permutations. All other relations follow from a deep relationship of Hurwitz numbers with moduli spaces of curves, Gromov-Witten invariants, matrix models, integrable systems and other domains of mathematics which are often referred to as `mathematical physics'. When discussing Hurwitz numbers in the talks, we consider them, thereby, as a sufficiently elementary but highly nontrivial model of all mentioned theories where all computations can be fulfilled completely, and all formulated relations can be checked explicitly in computer experiments.
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political recursion right now here which fortunately have to talks probably will postpone for tomorrow the system here few the question the the company was it's interviewed does exist for the DTP Aussie GP but not in this case because here a case those who be somewhat different not of of the and few me


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AV-Portal 3.16.0 (9cfa3864b8acb689056f9c67aa39bc8ec4c75d58)