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This workshop, sponsored by AIM and the NSF, will focus on the theory of Toeplitz matrices (TM) and Wiener-Hopf operators (WHO). In the recent ten or so years, the theory of these operators (TM and WHO) attracted a great deal of renewed attention from mathematical and theoretical physics communities due to the mathematical beauty of problems involved, and due to new applications in physics. For example, novel developments in quantum information theory and statistical physics concern the asymptotics of the (quantum) entanglement entropy of thermal equilibrium states, the overlap of ground states in the Anderson orthogonality catastrophe and the emptiness formation probability in quantum spin models. These quantities can be deduced from suitable Szego limit theorems, that is, from asymptotic results for traces of certain functions of TM and WHO.