Grothendieck's dessins d'enfants and the combinatorics of Coxeter groups

  • Goran Malic

Student thesis: Phd


In this thesis we study the properties of Lagrangian matroids of dessins d'enfants (also known as maps on orientable surfaces) and their behaviour under the action of the absolute Galois group Gal(Q). We show that while the Lagrangian matroid of a dessin itself is not invariant under this action, some of its properties, namely its width and parity, are. We also study the partial duals of a dessin and their Lagrangian matroids and show that certain partial duals can always be defined over their field of moduli. We prove some results on the representations of Lagrangian matroids as well.A relationship between dessins, their partial duals and tropical curves arising from monodromy groups of dessins is observed.
Date of Award1 Aug 2016
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorAlexandre Borovik (Supervisor) & Gabor Megyesi (Supervisor)


  • partial duals
  • maps on surfaces
  • tropical curve
  • absolute Galois group
  • Galois
  • matroid
  • dessin
  • Lagrangian matroid

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