| 13:30-14:30 | Yoshihiro Ohnita |
| Title: | Introduction to harmonic map theory as integrable systems |
| Abstract: | I will give an introductory survey on harmonic map theory of Riemann surfaces into Lie groups or symmetric spaces via related integrable system methods, such as loop groups/infinite dimensional Grassmannian models and Higgs bundle moduli spaces. |
| 14:50-16:20 | Alexander Bobenko |
| Title: | Orthogonal ring patterns and discrete cmc surfaces |
| Abstract: | We introduce orthogonal ring patterns consisting
of pairs of concentric circles. They generalize orthogonal circle
patterns which can be treated as conformal limit. It is shown that
orthogonal ring patterns in euclidean and hyperbolic planes and in
a sphere are governed by integrable equations. The variational
description is given in terms of elliptic generalizations of the
dilogarithm function. It is used to prove existence and uniqueness
results, and also to compute ring patterns with classical boundary
conditions. We define discrete constant mean curvature (cmc) surfaces
in the three-dimensional Euclidean and Lorentz spaces in terms of
sphere packings with orthogonally intersecting circles. These
discrete cmc surfaces can be constructed from orthogonal ring
patterns. The data used for the construction is purely combinatorial
- the combinatorics of the curvature line pattern. Numerous virtual
and printed models as well as animation movies will be demonstrated. (See the attached picture.) |
| 16:40-18:10 | Yuris Suris |
| Title: | On geometry of bilinear discretizations of quadratic vector fields |
| Abstract: | We discuss dynamics of birational maps which appear as bilinear discretizations of quadratic vector fields. Various aspects of integrability of birational dynamical systems will be discussed, along with remarkable geometric structures and constructions behind some of the particular examples. |