There has been huge surge of interest in topological aspects of condensed matter physics in the last ten years. More recently, it has started to transpire that the mathematics underlying this field has much in common with that used in and stimulated by string theory. This interdisciplinary confluence of ideas provides a rich source of new research directions, in both pure mathematics as well as mathematical physics, which this workshop aims to identify and develop. We specially target researchers with an interest in K-theory, noncommutative geometry, topology, and index theory, as well as their rigorous applications to string theory and topological matter in physics.