Enumeration of non-oriented dessins d'enfants

Time：13:00 - 15:00

Venue：A3-4-301

Organizer：Shamil Shakirov, Semen Artamonov, Pavel Nikitin, Yevgen Makedonskyi

Speaker：Maxim Karev

Speaker：Maxim Karev

Time：13:00 - 15:00

Venue：A3-4-301

Zoom：242 742 6089 (PW: BIMSA)

Organizers: Shamil Shakirov, Semen Artamonov, Pavel Nikitin, Yevgen Makedonskyi

Abstract

A classical Grothendieck dessin d'enfant is a proprely vertex-bicolored graph embedded in an oriented surface such that its complement is a union of disks. Equivalently, a dessin can be described by a triple of permutations in the symmetric group satisfying and a transitivity condition. Consequently, the enumeration of dessins d'enfants is equivalent to computing structure constants in the group algebra of .

In this talk, I will introduce the notion of a non-oriented dessin d'enfant, where the underlying surface is not required to be oriented. I will present an efficient recursion for counting such objects and identify the algebra whose structure constants encode their enumeration. Time permitting, I will also discuss an interpolation between the oriented and non-oriented cases.

DATEFebruary 25, 2026

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