Research

Research Outlook : Physical Mathematics, (T)QFT, String/M-Theory

I am interested in 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 (TQFTs); physical approaches to cohomological field theories.
Categorical and generalized symmetries.
Generalized cohomology theories in QFT/string/M-theory.
Supersymmetric gauge theories in curved space and supergravity.
Conformal field theory.

Topological field theory and generalized symmetries

Topological quantum field theories, physical approaches to cohomological field theories, higher-form fields, Gauss laws, and categorical/generalized symmetries.

Differential cohomology and K-theory

Applications of generalized cohomology theories to gauge fields, Ramond-Ramond fields, supergravity, and the global formulation of quantum field theories.

Supersymmetric gauge theories and four-manifold topology

Topological twisting of 4d N=2 theories, generalized spin-c structures, family Donaldson invariants, and curved-space supersymmetry.

String/M-theory and branes

M-theory fivebranes, M-theory and topology, 5d SCFTs from Calabi-Yau singularities, and geometric engineering.

TMF and low-dimensional SQFTs

Connections between two-dimensional N=(0,1) and N=(0,2) supersymmetric field theories, heterotic strings, and topological modular forms.

Current research

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.