Metric ribbon graphsMPIM

by Ivan Yakovlev (MPIM)

Tuesday Jul 15, 2025, 11:00 AM → 12:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Low-dimensional topology seminar

Metric ribbon graphs (MRG) are graphs embedded into surfaces equipped with positive edge lengths. Functions counting MRG's with given boundary lengths are a priori piecewise polynomials, but in some cases become honest polynomials.

I will first present one such case -- Kontsevich's polynomials counting trivalent MRG's (from his proof of Witten's conjecture about intersection numbers on the moduli spaces of curves), and explain how they are used to study hyperbolic and flat surfaces.

I will then describe other instances of this phenomenon that I have worked on, their applications, and a project to understand the combinatorics underlying the counting functions and the corresponding intersection numbers.