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Imagine a vibrating string. In mathematics, we would call this a one-dimensional motion (the dimension being the time over which the vibration occurs) of a one-dimensional object (the string) in three dimensions (our spatial universe). Mathematicians are interested in much more general music, where the object, the place in which it is vibrating and even the “time” over which it vibrates can all have many dimensions. Understanding the structure of such objects, which mathematicians call “spaces of embeddings”, is a basic question in the field of topology. Like much rich mathematics, it connects with many other areas in mathematics and beyond. These include the study of all possible ways to combine objects (operads), the study of quantities which can be defined through breaking things apart (topological field theories), and more elementary (but not easy!) subjects including graph theory and knot theory. In this workshop, we bring together researchers in all of these areas, who constitute a diverse collection of mathematicians (by time in career, gender, and nationality) to contemplate vibrating strings and their impact throughout mathematics and beyond.