Symmetries, anomalies, and non-perturbative string theory.

I study generalized symmetries through their realization in string theory, relating extended operators and topological defects to branes and the topology of compactification geometries. This includes non-invertible duality defects, K-theoretic descriptions of symmetry, and the effects of frozen singularities. I also use string junctions and anomaly constraints to investigate the global structure of gauge groups and the landscape of string vacua, with the aim of understanding what distinguishes consistent quantum theories of gravity.

I investigate how topological structures on the string worldsheet and in spacetime encode physical information. On the worldsheet side, this includes non-invertible symmetries and their gauging, as well as the spacetime selection rules associated with worldsheet fusion rules and their dependence on perturbative order. In spacetime, I study anomaly cancellation and inflow, discrete topological terms, and their descriptions using differential K- and KO-theory and index theory. These questions connect local anomaly computations with global consistency conditions.

I study renormalization-group flows and Higgs branches of supersymmetric quantum field theories, with a particular focus on six-dimensional superconformal theories and their lower-dimensional descendants. I combine low-energy effective actions with F-theory, brane constructions, and the geometry of nilpotent orbits to analyze symmetry breaking and relations between fixed points. Recent work develops systematic descriptions of minimal Higgsings and induced flows, and explores how these flows appear under compactification to four-dimensional class 𝒮 theories.