Igor Mezic University of California, Santa Barbara (UCSB) Two recent developments are gaining popularity in analysis of complex fluid flows: 1) The Koopman Mode Decomposition, and 2) Mesohyperbolicity analysis. I will describe the theory behind each of these and argue that their coupling is capable of describing mixing in complex, aperiodic flows using a strongly reduced representation - the Koopman Mode Decomposition - that enables application of both classical (e.g. lobe dynamics) and new, mesohyperbolicy-based tools to the problem of mixing in aperiodic flows.