Speaker: E. Yu. Bunkova (Steklov Mathematical Institute of Russian Academy of Sciences)

Title: Parametric Korteweg-de Vries hierarchy, polynomial dynamical systems and hyperelliptic sigma functions

Date and time:  12.11.2025, 17:00 (GMT +03:00)

Abstract: In our works with V. M. Buchstaber we have solved the problem of constructing dynamical systems corresponding to a hyperelliptic curve of infinite genus. In the talk the details of this construction will be presented. The dynamical systems in question are closely related to the famous Korteweg-de Vries hierarchy and a series of solutions of this hierarchy in terms of Kleinian hyperelliptic sigma functions. There are commutative diagrams giving embeddings of universal Jacobian bundles of hyperelliptic curves of any genus into a polynomial map of complex spaces of infinite dimension. The dynamical systems are explicit polynomial dynamical systems on these complex spaces, and the commutative diagrams bring them to differentiations of Abelian functions on the Jacobians of hyperelliptic curves.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com