Our group has a broad interest in soft matter problems that are governed by fundamental principles of geometry and topology. At one end of this spectrum are purely theoretical questions that involve exotic geometries and other physical and mathematical curiosities. At the other end is the application of soft matter principles and theories (liquid crystal theory, solid elasticity, fluid dynamics etc.) to the understanding of experimental observations and everyday problems. We use this approach to study the relations between local material order and emergent global shapes and patterns, in various contexts. Among these are programmable shape morphing and mechanical response of smart materials, topological defect architecture in liquid crystals, design of wrinkling patterns, and more.