# Seminar za teoriju reprezentacija ZCI QuantiXLie

lokacija:
PMF Matematički odsjek
vrijeme:
18.12.2018 - 17:15 - 18:30
Representation theory seminar and Center of Excellence QuantiXLie

Tuesday, December 18 at 17:15, room 109

Goran Malić:  Representation theory of dessins d'enfants

A dessin d'enfant is a connected graph embedded on a connected, closed and
orientable surface X. This embedding induces on X the structure of a
Riemann surface equipped with a holomorphic projection f to CP^1 ramified over
{0,1,\infty}. By Belyi's theorem X has the structure of a smooth
projective algebraic curve over the algebraic numbers. There is a natural
faithful action of the absolute Galois group Gal(\mathbb Q) on the set of
dessins d'enfants and a major goal is to understand the invariants of this
action.

Furthermore, the monodromy data of f induces on X a quiver Q and a bounded
path algebra kQ/I called a Brauer graph algebra, where I is an admissible
ideal of kQ given by the monodromy of f. This algebra captures some
essential information about (X,f) and allows us to use
representation-theoretic machinery to study the action of Gal(\mathbb Q) on
dessins d'enfants and construct new invariants. In particular, we can show
that Galois conjugate dessins d'enfants have derived equivalent Brauer
graph algebras.

This is joint work with
Sibylle Schroll.

Everybody is invited.

Karmen Grizelj