The principal research objectives of this project are to explore morphogenetic complexity of the equilibrium biphasic states of lyotropic chromonic liquid crystals (LCLCs) that require an implicit balance between the interfacial and bulk energy and to understand the mechanisms of coupling between the out-of-equilibrium behavior of living liquid crystals (LCs) and anisotropic interactions between the constituents, including the interplay of bacterial activity, bacterial concentration, vector field of velocities, and orientational order. These goals will be achieved through controlled experiments and theoretical modeling. In the case of an equilibrium behavior, a challenge is in finding the shapes of orientationally- and translationally-ordered structures in confined geometries, exemplified by the nuclei of the chromonic hexagonal columnar phase in the isotropic environment. The complex shapes observed in experiments need to be described through minimization of both the internal elastic bulk energy and the anisotropic surface anchoring energy. In the studies of dynamics of living liquid crystals (LLCs) the challenge is in simultaneous tracking of a number of scalar, vector, and tensor fields. The project aims to advance our ability to use mathematical algorithms for fast acquisition of big data characterizing dynamic systems with complex structure. It will also enhance predictive capabilities via the development and analysis of associated mathematical models.