On Generating Series of Cohomology of Generalized Configuration Spaces (Anton Khoroshkin, Haifa)

17.09.2024 16:30 – 17:30

A generalized configuration space on X consists of a collection of points on X with a prescribed rule determining which points may not coincide. I will introduce a new algebraic structure on the union of these spaces for X=R^n, which generalizes the concept of the little discs operad. I will demonstrate how one extracts information about the Hilbert series of cohomology rings out of this algebraic structure.
Surprisingly, the same method can be applied to obtain generating series for various combinatorial data associated with graphs, such as the number of Hamiltonian paths, Hamiltonian cycles, acyclic orientations, and chromatic polynomials.
If time permits, I will introduce certain compactifications of these configuration spaces for X=C that generalize the Deligne-Mumford compactification of the moduli spaces of rational curves with marked points, and I will present the formulas for the generating series of their cohomology.
The talk is based on the joint work with my student D.Lyskov: https://arxiv.org/abs/2406.05909

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire "Groupes de Lie et espaces de modules"

entrée libre