Annalisa Calini (College of Charleston, USA)
This talk will describe some natural geometric flows for curves and polygons in centro-affine geometry, and their relations with the KdV and Boussinesq equations and discretizations of Adler-Gel’fand-Dikii (AGD) flows for curves in projective space. The AGD discretizations (previously introduced in work by Marí-Beffa and Wang) will be discussed in more detail, as their lifts to the moduli space of centro-affine arc length parametrized polygons promptly reveal their bihamiltonian structures in terms of a pair of simple pre-symplectic forms.
Some references:
U. Pinkall, Hamiltonian flows on the space of star-shaped curves, Result. Math. 27 (1995), 328–332.
A. Calini, T. Ivey, and G. Marí-Beffa, Remarks on KdV-type Flows on Star-Shaped Curves, Physica D Vol. 238, no. 8 (2009), 788–797
G. Marí-Beffa and J.P. Wang, Hamiltonian structures and integrable evolutions of twisted gons in RPn, Nonlinearity 26 (2013) 2515-2551
A. Calini, T. Ivey, and G. Marí-Beffa, An integrable flow for starlike curves in centroaffine space, SIGMA 9, (2013), 022, 21 pp.
A. Calini and G. Marí-Beffa, Integrable evolutions of twisted polygons in centroaffine Rm, IMRN, rnaa161 (2020)