Reconfiguration of square-tiled surfaces
Clément Legrand-Duchesne
Université Jagiellonian (Cracovie, Pologne)
https://johnlepoulpe.github.io/
Date(s) : 16/01/2026 iCal
11h00 - 12h00
We consider a combinatorial reconfiguration problem on a subclass of quadrangulations of surfaces called square-tiled surfaces. Our elementary move is a shear in a cylinder that corresponds to a well-chosen sequence of diagonal flips that preserves the square-tiled properties. We conjecture that the connected components of this reconfiguration problem are in bijection with the connected components of the moduli space of quadratic differentials. We prove that the conjecture holds in the so-called hyperelliptic components of Abelian square-tiled surfaces. More precisely, we show that any two such square-tiled surfaces of genus g can be con be connected by O(g) powers of cylinder shears.
This is joint work with Vincent Delecroix.
Emplacement
Saint-Charles - FRUMAM (2ème étage)
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