University of Chicago

Many phenomena in nature, from complex flows to the ways materials self-assemble and break, are underpinned by elegant geometric and topological mechanisms. A focus of our research, that spans soft condensed matter, optics and topological fluid mechanics is to seek and unravel the presence of these powerful interpretative keys.

One example is the experimental and theoretical study of "knotted fields". The possibility of localized knottedness in a space-filling field has fascinated physicists and mathematicians ever since Kelvin's 'vortex atom' hypothesis, in which the atoms of the periodic table were hypothesized to correspond to knotted vortex loops in the aether -- akin to smoke rings, tied into knots. Knotted vortices, or tangles of magnetic field lines, have re-emerged in modern interpretations of plasma and both classical and superfluid complex flows. We seek to understand the physics and broader role of these fascinating excitations through experiments on knotted and shaped vortices in water, and studies of the the mathematical structure of knots in fields.

Similarly, geometric and topological constraints can provide a powerful interpretative key in understanding the behavior of many condensed matter systems - from topological defects in ordered phases, to the self-assembly of structures driven by the geometry of the constituents, to the relationship between chiral geometry and physical response. Conversely, these interpretative keys can be used to control the properties and assembly of materials. We study this interplay using soft condensed matter systems. ''Soft'' is used to describe a rich variety of classical many-body and material systems that have energetics accessible at room temperature and can be imaged. Our experiments are based on micron sized colloids, elastic sheets, foams and gels. We use them to study phenomena from self-assembly to shocks and fracture.

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