The Center for Mathematics of Living and Mimetic Matter brings together leading scientists from Pennsylvania State University that work across many disciplines – mathematicians, chemists, biologists, materials scientists and engineers with an important mission: develop a much better understanding dynamic processes occurring in living and mimetic matter under out-of-equilibrium conditions. The systems under study are exemplified by suspensions of motile microorganisms, cell tissues, synthetic swimmers and nanomotors. These systems inspire the design of new generation of synthetic materials that exhibit life-like behavior: adapting their functionality to changes in the environment, harvesting energy from their surroundings, and undergoing self-repair. А synergy of applied mathematics, state-of-the-art computational modeling, and dedicated experiment will provide a transformative change in our understanding of the non-equilibrium processes and emergent behavior at the interface of engineering, life and mathematical sciences.