Двумерные клеточные комплексы, вещественные числа Гурвица и интегрируемые системы2-dimensional cell complexes, real Hurwitz numbers and integrable systems

A classical problem going back to the XIX-th century works by A.Hurwitz et al. is to count meromorphic functions with prescribed singularities on complex curves. Most results of the thesis deal with ramifications of this problem: the curves with real structure, complicated singularities and counting with weights. These results occupy mostly Chapters 1 and 3 of the thesis. The analysis of the problems involves some results of combinatorics similar to the classical matrix-tree theorem by G.Kirchhoff (1847). The thesis contains numerous generalizations of this theorem, too, mostly found in Chapter 2.