Session I.5 - Geometric Integration and Computational Mechanics
Tuesday, June 13, 17:00 ~ 17:30
Geometric Integration and Numerical Analysis on Symmetric Spaces
Hans Munthe-Kaas
Lie-Størmer Center at The Arctic University of Norway, Norway - This email address is being protected from spambots. You need JavaScript enabled to view it.
Symmetric spaces are spaces equipped with a symmetric product. In differential geometry, prime examples are spheres, hyperbolic spaces and Grassman manifolds. Together with Reinout Quispel and Antonella Zanna, we have explored many properties of spaces with a symmetric product, in works going back two decades. After a brief survey of this body of work, I will discuss a new canonical numerical time integration algorithm on symmetric spaces and discuss recent work on understanding the algebras of canonical connections on symmetric spaces, torsion free, with constant curvature, where the goal is to develop a theory of B-series on symmetric spaces.
Joint work with Jonatan Stava, University of Bergen.