Abstract: On the basis of final reports submitted by all eligible participants in last summer's REGS program, three Fellows were selected to give 15-minute presentations on their projects: - Anton Lukyanenko
Title: Embedding spheres in Heisenberg space using hyperbolic geometry
Abstract: A sub-Riemannian space models motion that is constrained locally, but not globally, like that of a car trying to parallel park. The basic example of a sub-Riemannian space is the Heisenberg group. This summer, we used its connection to complex hyperbolic geometry to construct bi-Lipschitz embeddings of spheres into the Heisenberg group. We then used these embeddings to construct examples of functions that display the relationship between the analysis and geometry of the space. - Matthew Yancy
Title: A Few Results on a Monotonic Sequence Game
Abstract: We will define a two-player game played on a poset where victory occurs by being the first to construct a chain of fixed size. Results for completely known posets are already known, we will provide results on more complicated structures. - Chris Appuhn
Title: Complex-Tangential Curves in S(2n-1)
Abstract: A curve contained in a real hypersurface in Cn is called complex-tangential if its derivative lies in the complex tangent space at each point. We examine complex-tangential curves lying in the unit sphere. A. Iordan proved a sufficient condition for such curves in S3 to have constant curvature. We show that this result fails in higher dimensions and consider possible generalizations. |
|
