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My research interests lie in commutative algebra and algebraic geometry. In particular, I study invariants of singularities of algebraic varieties. These include multiplier ideals, log canonical thresholds and jumping numbers in characteristic zero, and test ideals, F-pure thresholds and the F-signature in positive characteristics. Recently, I have also been interested in K-stability and the geometry of Fano varieties.
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Most of my recent research has involved the F-signature, an invariant that captures asymptotic properties of the Frobenius map. I have been studying the F-signature from a geometric viewpoint, which allows us to connect the F-signature to ideas and techniques from birational geometry.