Symmetry and modularity

Motives, modularity, and mirror symmetry

We consider certain families of Calabi-Yau orbifolds and their mirror partners constructed from Fermat hypersurfaces in weighted projective spaces. We use Fermat motives to interpret the topological mirror symmetry phenomenon. These Calabi-Yau orbifolds are defined over Q, and we can discuss the modularity of the associated Galois representations. We address the modularity question at the motiv...

A Modularity Test for Elliptic Mirror Symmetry

In this note a prediction of an algebraic mirror construction is checked for elliptic curves of Brieskorn-Pham type via number theoretic methods. It is shown that the modular forms associated to the Hasse-Weil L-series of mirror pairs of such curves are identical. PACS Numbers and

Forcing Neurocontrollers to Exploit Sensory Symmetry Through Hard-wired Modularity in the Game of Cellz

Several attempts have been made in the past to construct encoding schemes that allow modularity to emerge in evolving systems, but success is limited. We believe that in order to create successful and scalable encodings for emerging modularity, we first need to explore the benefits of different types of modularity by hard-wiring these into evolvable systems. In this paper we explore different w...

The Business of Modularity and the Modularity of Business

Symmetry of Fullerene C_60