Speaker
Dmitrii Korshunov
(Institut de mathématiques de Jussieu – Paris Rive Gauche)
Description
Consider all closed polygonal paths in three-dimensional Euclidean space
consisting of n edges of prescribed lengths. We identify those that are
related by an isometry of R^3. This moduli space carries a Kähler
structure (Deligne–Mostow, Klyachko, Kapovich–Millson). I will discuss
the relation between the symplectic geometry of this moduli space,
flexible polyhedra, and a solution of Kenyon’s problem on triangulated
domes. If time permits, we will discuss the heuristic similarity of this
space to Teichmüller space and the moduli space of flat surfaces,
together with the probabilistic questions it suggests about the expected
shape of random polygonal paths.
Author
Dmitrii Korshunov
(Institut de mathématiques de Jussieu – Paris Rive Gauche)