Abstract:
Rational parametrizations play a crucial role in algebraic geometry. In differential algebra, a similar concept is that of so-called realizations. In this talk we see when and how realizations and its inverse operation, implicitization, can be successfully performed, which is strongly linked to finding rational parametrizations. We will also consider the problems of finding polynomial realizations and that of realizations involving parameters in an optimal way.
This talk is based on joint works with Rafael Sendra, Alexey Ovchinnikov and Dmitrii Pavlov.