Natural systems provide both puzzles to unravel and demonstrations of what's possible. The natural world is full of complex systems of dynamically interchangeable, individually unreliable components that produce effective and reliable outcomes at the group level. A complementary goal to understanding the operation of such systems is that of being able to engineer artifacts that work in a similar way. One notable type of collective behavior is collective construction, epitomized by mound-building termites, which build towering, intricate mounds through the joint activity of millions of independent and limited insects. The artificial counterpart would be swarms of robots designed to build human-relevant structures. I will discuss work on both aspects of the problem, including studies of cues that individual termite workers use to help direct their actions and coordinate colony activity, and development of robot systems that build user-specified structures despite limited information and unpredictable variability in the process. These examples illustrate principles used by the insects and show how they can be applied in systems we create.

The spontaneous collective motion of self-propelled agents is ubiquitous in the natural world, and it often occurs in complex environments, be it bacteria and cells migrating through polymeric extracellular matrix or animal herds and human crowds navigating structured terrains. Much is known about flocking dynamics in pristine backgrounds, but how do spatio-temporal heterogeneities in the environment impact such collective self-organization? I will present two model systems, a colloidal active fluid negotiating disordered obstacles and a confined dense bacterial suspension in a viscoelastic medium, as controllable platforms to explore this question and highlight general mechanisms for active self-organization in complex environments. By combining theory and experiment, I will show how flocks on disordered substrates organize into a novel dynamic vortex glass phase, akin to vortex glasses in dirty superconductors, while the presence of viscoelasticity can calm the otherwise turbulent swarming of bacteria, allowing the emergence of a large scale coherent and even oscillatory vortex when confined on the millimetre scale.

Diversity in the natural world emerges from the collective behavior of large numbers of interacting objects. Statistical physics provides the framework relating microscopic to macroscopic properties. A fundamental assumption underlying this approach is that we have complete knowledge of the interactions between the microscopic entities. But what if that, even though possible in principle becomes impossible in practice ? Can we still construct a framework for describing their collective behavior ? Dense suspensions and granular materials are two often quoted examples where we face this challenge. These are systems where because of the complicated surface properties of particles there is extreme sensitivity of the interactions to particle positions. In this talk, I will present a perspective based on notions of constraint satisfaction that provides a way forward. I will focus on our recent work on the emergence of elasticity in the absence of any broken symmetry, and sketch out other problems that can be addressed using this perspective.