I will review recent exciting progress in (1) geometric and algebraic graph
theory on the torus, including modeling, algebraic and topological results,
(2) multistability in flow and elastic networks, including paradoxes in
lossy coupled oscillators, and (3) synchronization of diffusively coupled
dynamics. The combined geometric, analytic and computational approach is
based on the nexus of convex optimization, monotone operators and
contraction theory. Moreover, I will speculate on open problems in the
context of (i) fundamental theory of phase-space and state-space coupled
oscillators, (ii) applications to energy systems, including power flows and
optimization, and (iii) applications to machine learning and neuroscience
(associative memory, architectures, and learning).