Jan

23

2017

Jan

23

2017

Every compact connected 2-manifold N can be expressed as the orbit space determined by a group of isometries G acting freely and properly discontinuously on a Riemannian 2-manifold M which is either the 2-sphere, the Euclidean plane, or the PoincarĂ© disk. In each case, M is simply connected, and so the fundamental group of N is isomorphic to G.

Jan

23

2017

Complex Systems interview talk.

Jan

23

2017

Plasmonic structures are made of dielectrics and metals, and at optical frequencies metals exhibit unusual electromagnetic properties like a negative dielectric permittivity whereas dielectrics have a positive one. This change of sign allows the propagation of electromagnetic surface waves at the metal-dielectric interface, where strange phenomena appear if it presents corners.

Jan

24

2017

With Calta and Kraaikamp, we define and study $\alpha$-type maps $T_{n,\alpha}$ for each of a countable number of (Fuchsian triangle) groups (thus playing the role of $\text{PSL}_2(\mathbb Z)$); these groups are defined over number fields (whose degree is unbounded). We show that the key property of orbit synchronization of the endpoints of the interval of definition holds for each $n$ on a set of $\alpha$ of full measure, and identify cross-sections for these $T_{n,\alpha}$.

In this second talk, we aim to sketch proofs of some of the main results.