Prize Talk: Prize for a Faculty Member for Research in an Undergraduate Institution"Building electronic lattices and networks to explore the interplay between geometry and nonlinearity"

Emergence says that new phenomena can arise when familiar building blocks are assembled into larger systems. In this talk, the building blocks will be things like capacitors, inductors, diodes, and op-amps, the systems will be lattices and networks, and the phenomena will range from oscillator synchronization to spin-glass-like frustration, and from spontaneous energy localization to flat-band physics. An advantage of these electronic systems is the versatility they afford in geometric design, allowing us to engineer specific dispersion relations, for instance, as well as the feasibility of infusing these systems with nonlinearity of various types. Another strength is the experimental accessibility of the detailed nonlinear dynamics these systems exhibit. As such, they provide an ideal playground for exploring the interplay between geometry and nonlinearity. From a broader perspective, this arena also illustrates the beneficial confluence of experimental, theoretical, and numerical approaches and showcases the potential of undergraduate research.