Seminario: Pentagram maps and nondegenerate curves

Lunedi` 30 giugno 2014, ore 12:00 Sala Riunioni VII piano - Boris Khesin (University of Toronto)

ARGOMENTI: Seminari Display

Titolo: "Pentagram maps and nondegenerate curves"

Autore del seminario: Boris Khesin (University of Toronto)

Data: Lunedi` 30 giugno 2014, ore 12:00
Aula: Sala Riunioni VII piano

ABSTRACT: A plane curve is called nondegenerate if it has no inflection
points. How many classes of closed nondegenerate curves exist on a
sphere? We are going to see how this geometric problem, solved in 1970,
reappeared along with its generalizations in the context of the
Korteweg-de Vries and Boussinesq equations. Its discrete version is
related to the 2D pentagram map defined by R.Schwartz in 1992. We will
also describe its generalizations, pentagram maps on polygons in any
dimension and discuss their integrability properties.
This is a joint work with Fedor Soloviev.