Rationalizing Euclidean Assemblies of Hard Polyhedra from Tessellations in Curved Space Entropic self-assembly is governed by the shape of the constituent particles, yet a prioriprediction of crystal structures from particle shape alone is non-trivial for anything but thesimplest of space-filling shapes. At the same time, most polyhedra are not space fillingdue […]
Circle packing in regular polygons  We discuss algorithms that allow one to generate configurations of congruent circles inside a regular polygon and present numerical results for polygons with up to 16 sides. Some general properties of these configurations will be highlighted and the topological charge associated with their Voronoi diagrams […]
Hyperuniformity and Particle Packings The study of hyperuniform states of matter is an emerging multidisciplinary field, influencing and linking developments across the physical sciences, mathematics and biology. A hyperuniform point process in d-dimensional Euclidean space is characterized by an anomalous suppression of large-scale density fluctuations relative to those in typical […]
Arrangements of spheres in transverse confinement Much work has been done on the study of structures formed by both hard and soft spheres held in transverse confining potentials [1, 2, 3]. These structures self-assemble under the action of their confining potentials, forming interesting columnar structures. Here we will present an […]
Geometric Design of Kirigami Metamaterials  Kirigami, the traditional art of paper cutting, has recently emerged as a promising paradigm for mechanical metamaterials. While many prior works have studied the geometry and mechanics of certain periodic kirigami tessellations, the computational design of more complex structures is less understood. In this talk, […]
Effective Geometries in Elasticity: Wrinkled Shells and Shape-Morphing Kirigami What do wrinkled shells and shape-morphing kirigami sheets have in common? The answer is fine scale buckling — a patterned response driven by mechanical instabilities enabling macroscopic shape change beyond bulk elasticity. This talk will present two recent developments on (i) […]
Optimal packing of a finite collection of deformable objects How should space-filling, deformable objects be packed so as to minimize the area of the interfaces between them? In 3D the search for a packing of equal-volume shapes with minimum surface area is known as the Kelvin problem. In 2D the […]
Measures of order for imperfect two-dimensional patterns Motivated by patterns with defects in natural and laboratory systems, we develop two quantitative measures of order for imperfect Bravais lattices in the plane. A tool from topological data analysis called persistent homology combined with the sliced Wasserstein distance, a metric on point […]
Mathematical Modelling of Programmable Polymorphism of Protein Cages Protein cages, convex polyhedral protein containers self-assembled from multiple copies of identical protein subunits, are pillars of nanotechnology. They include naturally occurring virus capsids (virus-like particles, VLPs) which are spherical as well as a plethora of particles with diverse symmetries such as […]
Cumulative Geometric Frustration and the Intrinsic Approach to Physical Assemblies Geometric frustration arises whenever the constituents of a physical assembly locally favor an arrangement that is incompatible with the geometry or topology of the space in which it resides.  It naturally arises in a variety of fields ranging from macromolecular assemblies to liquid-crystals to spin models, yet in distinct systems, geometric frustration may […]