I work on quantum field theory, string theory, and Physical Mathematics. For some background about the latter, please refer to the following articles:
I like to think of this pursuit more generally as the application of physics to mathematics. Broadly, my interests include, in no particular order:
Topological quantum field theories, physical approaches to cohomological field theories, higher-form fields, Gauss laws, and categorical/generalized symmetries, with an emphasis on their interplay with spacetime topology and geometry.
Applications of generalized cohomology theories to gauge fields, Ramond-Ramond fields, supergravity, and the global formulation of quantum field theories. Electromagnetic duality and the global definition of partition functions, with ongoing work connecting differential cohomology, derived geometry, and determinant lines.
Topological twisting of 4d N=2 theories, including non-Lagrangian theories, generalized spin-c structures, family Donaldson invariants of smooth families of four-manifolds, and curved-space supersymmetry.
M-theory fivebranes, M-theory and topology, 5d SCFTs from Calabi-Yau singularities, and geometric engineering. Global aspects of the M-theory C-field, cubic refinements, Page charges, and fivebrane partition functions.
Connections between two-dimensional N=(0,1) and N=(0,2) supersymmetric field theories, heterotic strings, and topological modular forms. String dualities and worldsheet renormalization-group flows as tools for detecting torsion in TMF.
My current research is on TQFTs, generalized symmetries, aspects of 2d N=(0,2) and N=(0,1) sigma models and connections to Topological Modular Forms, and applications of differential cohomology and K-theory to Ramond-Ramond fields in supergravity.
I have worked on an extension of Donaldson-Witten Theory to smooth families of closed, oriented Riemannian 4-manifolds, leading to a physics-inspired proposal for Family Donaldson Invariants. In the past, I have worked on geometric engineering of five-dimensional gauge theories from M-theory.