Chennai Mathematical Institute


Research seminar by MSc students
11:50 - 1:05, Seminar Hall
Geometry of the moduli space of polygons

Sambit Senapati
Chennai Mathematical Institute.


The moduli space of polygons is defined to be the space of closed piecewise linear paths in R^2 or R^3 modulo orientation preserving isometries. They can be realised as quotients of Grassmannians. If we further fix the length of each step, the moduli spaces M_r so obtained can be seen as symplectic quotients. These are always complex analytic and for generic and proper edge-lengths they are even Kähler. If time permits, I'll define a Hamiltonian torus action on M_r obtained by ``bending diagonals" and provide ``action-angle coordinates".