Richard P. Stanley Seminar in Combinatorics: Permutohedral complexes and curves with cyclic action

There is a beautiful story connecting the permutohedron to several different objects in algebra, geometry, and combinatorics: namely, to the symmetric group, to the geometry of a particular moduli space of curves, and to the theory of matroids.  Somewhat more recently, the analogue of this story in type B was developed, where the role of the permutohedron is played by the signed permutohedron and the corresponding moduli space parameterizes curves with an involution.  I will discuss joint work with C. Damiolini, C. Eur, D. Huang, S. Li, and R. Ramadas that develops a further generalization, defining a “permutohedral complex” that relates to a certain family of complex reflection groups, to the geometry of a moduli space of curves with finite-order automorphism, and to the combinatorics of multimatroid

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