As part of the Simons Collaboration for Special Holonomy in Geometry, Analysis, and Physics, I worked at the intersection of mathematics and physics to incorporate new research on special holonomy spaces into string theory constructions. My dissertation studies the duality between M-theory on $G_2$ manifolds and the $E_8 \times E_8$ heterotic string on Calabi-Yau threefolds. At low energies, each side of this duality gives an effective $N=1$ supersymmetric description of our universe, and in favorable situations, the background geometry and bundles may be chosen in a way that the two descriptions coincide. My work explored this correspondence both on orbifolds and in local models of the relevant geometries. Current projects:
- The Reduced Hull-Strominger System: With Eirik Eik Svanes and Bobby Acharya, I studied solutions to the Hull-Strominger system reduced to the 3D base of a local model of a Calabi-Yau threefold. Click here to view an arXiv preprint of our paper.
- Duality on Orbifolds: With David Morrison and Bobby Acharya, I studied how M-theory/heterotic duality behaves in the case of the half-$G_2$ limit of a $G_2$ orbifold. Click here to view an arXiv preprint of our paper.
Quantum Gravity and Holography
Before specializing to string theory, I studied more general aspects of quantum gravity from the point of view of holography and the gravitational path integral.
- Observables in AdS: With Steve Giddings, I studied diffeomorphism-invariant observables in anti-de Sitter spacetimes and the role of gravitational dressings in holography. You can view the paper in JHEP here or the arXiv preprint here.
- Wormhole Instantons: With Sean Hartnoll, I completed an undergraduate honors thesis on the perturbations about an axionic wormhole gravitational instanton, which can be viewed here.
Throughout my undergraduate degree, I conducted research in earthquake seismology. These formative years cemented my passion for the earth sciences.
- Rough Faults: With Eric Dunham, I investigated the effects of fault roughness on the radiation pattern of earthquakes. This work was supported by a Stanford Undergraduate Research Major Grant.
- Soil-Structure Interaction: With Eric Dunham, I studied the fully-coupled interaction of seismic waves with buildings in an idealized model. This work was presented at the 2013 Southern California Earthquake Center Annual Meeting. Click here for the poster.
- Mantle Anisotropy: With Simon Klemperer and Shahar Barak, I studied mantle anisotropy via shear wave splitting observed in the Salton Trough in Southern California. This work was presented at the AGU 2012 Annual Meeting, and the poster can be viewed here.