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Royce studies spherical virtual knots, a concept defined and explored by his summer research students. Characterizing these knots relies on interplay between combinatorics, topology and algebra. Royce plays piano and gives recitals on a regular basis, both solo and with others. He provides percussive harmony on the keyboard for the Prairie Jewels, a local Dixieland band. The best way to do well in Royce's classes is to ask lots of questions.