We develop a nonperturbative, functorial theory of defects in Abelian Chern–Simons theory on surfaces of arbitrary genus, showing that the finite quadratic module controls not only the bulk TQFT but also its boundaries, domain walls, condensations, and defects. We also establish an Alterfold/Chern–Simons dictionary. We further show that reciprocity does not generally define a TQFT duality, contrary to recent claims in the literature. Together, these results provide an explicit, unified realization of the Abelian defect structure, bringing previously separate gauge-theoretic and categorical descriptions into a single TQFT framework.

We show that Berry data measured on a torus are enough to determine the full all-genus Abelian topological theory, including its defects. This puts a long-standing piece of folklore in Abelian topological order on rigorous footing.

We classify Abelian Chern–Simons theories and show that their TQFT structure is encoded by a finite quadratic module.

We show that toral Chern–Simons theory and its Reshetikhin–Turaev counterpart are equivalent as TQFTs. Earlier work established relations only at the level of partition functions or mapping-class-group representations; to our knowledge, this is the first explicit proof of the expected equivalence at the level of the full, nonperturbative TQFT.

We construct toral Chern–Simons theory through geometric quantization and show that it leads to a well-defined nonperturbative TQFT. This provides a rigorous mathematical foundation for describing Abelian topological order on surfaces of arbitrary genus.

We give a rigorous construction of the Chern–Simons path integral and show that it produces a consistent nonperturbative topological quantum field theory.

We show that U(1) Chern–Simons theory and its Reshetikhin–Turaev counterpart are equivalent at the level of TQFT. 

We complete the calculation of electromagnetic corrections to semileptonic kaon decays and use it to obtain a more precise determination of |Vus|.

We combine improved theory and experimental data from kaon and pion decays to test the consistency of quark mixing in the Standard Model.

We calculate electromagnetic corrections to Ke3 decays with much higher precision and show that they cannot explain the existing discrepancy in |Vus|.

We improve the precision of the electromagnetic corrections to Ke3 decays by about an order of magnitude, reducing an important uncertainty in |Vus|.

We develop a new framework for computing electroweak corrections in semileptonic kaon decays, with the goal of extracting |Vus| more precisely.

We study partially massless gravity in three dimensions and show how adding a Chern–Simons term connects it to self-dual massive gravity.